A228338 Third diagonal of Catalan difference table (A059346).

5, 9, 19, 43, 102, 250, 628, 1608, 4181, 11009, 29295, 78655, 212815, 579675, 1588245, 4374285, 12103407, 33628827, 93786969, 262450881, 736710360, 2073834420, 5853011850, 16558618510, 46949351275, 133390812255, 379708642289, 1082797114049, 3092894319078, 8848275403642

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Jocelyn Quaintance and Harris Kwong, A combinatorial interpretation of the Catalan and Bell number difference tables, Integers, 13 (2013), #A29.

Formula

From Vaclav Kotesovec, Feb 14 2014: (Start)

Recurrence: (n+4)*a(n) = (2*n+7)*a(n-1) + 3*(n-1)*a(n-2).

G.f.: -(x+1)^(5/2)*sqrt(1-3*x)/(2*x^4)-1/2*(-1-x+3*x^2+7*x^3)/x^4.

a(n) ~ 8 * 3^(n+3/2) / (sqrt(Pi) * n^(3/2)). (End)

a(n) = 5*(-1)^n*hypergeom([7/2, -n], [5], 4). - Peter Luschny, May 25 2021

Maple

a := n -> 5*(-1)^n*hypergeom([7/2, -n], [5], 4):
seq(simplify(a(n)), n=0..29); # Peter Luschny, May 25 2021

Mathematica

CoefficientList[Series[-(x+1)^(5/2)*Sqrt[1-3*x]/(2*x^4)-1/2*(- 1 - x + 3*x^2 + 7*x^3)/x^4, {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 14 2014 *)

Prog

(PARI) x='x+O('x^50); Vec(-(x+1)^(5/2)*sqrt(1-3*x)/(2*x^4)-1/2*(-1-x+3*x^2+7*x^3)/x^4) \\ G. C. Greubel, May 31 2017

Crossrefs

Cf. A059346, A001006, A005043, A005554.

Sequence in context: A282730 A082674 A292773 * A309731 A253951 A102172

Adjacent sequences: A228335 A228336 A228337 * A228339 A228340 A228341

Keyword

nonn

Author

N. J. A. Sloane, Aug 29 2013

Extensions

Terms a(21) onward added by G. C. Greubel, May 31 2017

Status

approved