A076036 G.f.: 1/(1 - 5*x*C(x)), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) = g.f. for the Catalan numbers A000108.

1, 5, 30, 185, 1150, 7170, 44760, 279585, 1746870, 10916150, 68219860, 426353130, 2664633580, 16653699860, 104084695500, 650526003825, 4065775405350, 25411052086350, 158818913483700, 992617612224750, 6203857867325700, 38774103465635100, 242338116077385600

Offset

0,2

Comments

Numbers have the same parity as the Catalan numbers, that is, a(n) is even except for n of the form 2^m - 1. Follows from C(x) = 1/(1 - x*C(x)) = 1/(1 - 5*x*C(x)) (mod 2). - Peter Bala, Jul 24 2016

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k = 0..n} A106566(n, k)*5^k. - Philippe Deléham, Sep 01 2005

a(n) = Sum{k = 0..n} A039599(n,k)*4^k. - Philippe Deléham, Sep 08 2007

a(0) = 1, a(n) = (25*a(n-1) - 5*A000108(n-1))/4 for n >= 1. - Philippe Deléham, Nov 27 2007

a(n) = Sum_{k = 0..n} A116395(n,k)*3^k. - Philippe Deléham, Sep 27 2009

D-finite with recurrence: +4*n*a(n) +(-41*n+24)*a(n-1) +50*(2*n-3)*a(n-2)=0. - R. J. Mathar, Jan 20 2020

a(n) = 5*A076025(n), n>0. - R. J. Mathar, Jan 20 2020

Prog

(PARI) C(x) = (1 - sqrt(1 - 4*x))/(2*x);
my(x = 'x + O('x^25)); Vec(1/(1 - 5*x*C(x))) \\ Michel Marcus, Jan 21 2020

Crossrefs

Cf. A000108, A000984, A007854, A076035, A126694.

Sequence in context: A227383 A155195 A147837 * A195257 A161407 A006773

Adjacent sequences: A076033 A076034 A076035 * A076037 A076038 A076039

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 29 2002

Status

approved