A006636 From generalized Catalan numbers. (Formerly M4516)

8, 36, 102, 231, 456, 819, 1372, 2178, 3312, 4862, 6930, 9633, 13104, 17493, 22968, 29716, 37944, 47880, 59774, 73899, 90552, 110055, 132756, 159030, 189280, 223938, 263466, 308357, 359136, 416361, 480624, 552552, 632808, 722092, 821142, 930735

Offset

0,1

References

H. M. Finucan, Some decompositions of generalized Catalan numbers, pp. 275-293 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. Oates-Williams and A. P. Street. Lecture Notes Math., 952. Springer-Verlag, 1982.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..35.

A. G. Shannon, Catalan triangles and Finucan's hidden folders. Notes on Number Theory and Discrete Mathematics, 22(2), 10-16, (2016).

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

From Sean A. Irvine, May 30 2017: (Start)

a(n) = (n + 1)*(n + 2)*(n + 4)*(n + 8)*(n + 15)/120.

G.f: (2 - x)^3/(x - 1)^6. (End)

E.g.f.: exp(x)*(960 + 3360*x + 2280*x^2 + 500*x^3 + 40*x^4 + x^5)/120. - Stefano Spezia, Oct 15 2022

Crossrefs

Cf. A181289.

Sequence in context: A245360 A032768 A224410 * A325656 A357716 A341987

Adjacent sequences: A006633 A006634 A006635 * A006637 A006638 A006639

Keyword

nonn,easy

Author

Simon Plouffe

Extensions

a(6) and a(8) corrected and more terms from Sean A. Irvine, May 30 2017

Status

approved