The Hankel Transform of the Sum of Consecutive Generalized Catalan Numbers

نویسندگان

  • Predrag Rajković
  • Marko D. Petković
چکیده

X iv :m at h/ 06 04 42 2v 1 [ m at h. C O ] 1 9 A pr 2 00 6 The Hankel Transform of the Sum of Consecutive Generalized Catalan Numbers Predrag Rajković, Marko D. Petković, University of Nǐs, Serbia and Montenegro Paul Barry School of Science, Waterford Institute of Technology, Ireland Abstract. We discuss the properties of the Hankel transformation of a sequence whose elements are the sums of consecutive generalized Catalan numbers and find their values in the closed form. Mathematics Subject Classification: 11Y55 , 34A25

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Generalized Catalan Numbers and Generalized Hankel Transformations

so that an is the sum of the n th and n + 1 Catalan numbers. Then the Hankel transform of {a0, a1, a2, . . .} begins 2, 5, 13, 34, . . .. Layman first conjectured in the On-Line Encyclopedia of Integer Sequences ([4], see sequence A001906) that this sequence consists of every other Fibonacci number, and subsequently Cvetković, Rajković and Ivković [2] proved this conjecture. The current paper a...

متن کامل

Combinatorics of Generalized Motzkin Numbers

The generalized Motzkin numbers are common generalizations of the Motzkin numbers and the Catalan numbers. We investigate their combinatorial properties, including the combinatorial interpretation, the recurrence relation, the binomial transform, the Hankel transform, the log-convexity, the continued fraction of the generating function, and the total positivity of the corresponding Hankel matrix.

متن کامل

Generalized Catalan Numbers, Hankel Transforms and Somos-4 Sequences

We study families of generalized Catalan numbers, defined by convolution recurrence equations. We explore their relations to series reversion, Riordan array transforms, and in a special case, to Somos-4 sequences via the mechanism of the Hankel transform.

متن کامل

Hankel Determinant Solution for Elliptic Sequence

We show that the Hankel determinants of a generalized Catalan sequence satisfy the equations of the elliptic sequence. As a consequence, the coordinates of the multiples of an arbitrary point on the elliptic curve are expressed by the Hankel determinants. PACS numbers: 02.30.Ik, 02.30.Gp, 02.30.Lt

متن کامل

Some Relations Between Generalized Fibonacci and Catalan Numbers

In a recent paper Aleksandar Cvetkovi c, Predrag Rajkovi c and Miloš Ivkovi c proved that for the Catalan numbers Cn the Hankel determinants of the sequence Cn þ Cnþ1 are Fibonacci numbers. Their proof depends on special properties of the corresponding orthogonal polynomials. In this paper we give a generalization of their result by other methods in order to give more insight into the situation...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007