A035045 Inverse binomial transform of A002054.

1, 4, 12, 35, 101, 291, 839, 2423, 7011, 20326, 59038, 171777, 500603, 1461032, 4269828, 12493857, 36599403, 107325540, 315027276, 925501857, 2721208599, 8007114171, 23577440439, 69470880381, 204821487269, 604223501426, 1783419354954, 5266582196407, 15560042628205

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A005774.

Programs

Mathematica

Table[Sum[(-1)^(n-k)*Binomial[n,k]*Binomial[2k+3,k],{k,0,n}],{n,0,22}] (* Vaclav Kotesovec, Oct 08 2012 *)

PARI

a(n)=sum(k=0,n,(-1)^(n-k)*binomial(n,k)*binomial(2*k+3,k) ); \\ Joerg Arndt, May 04 2013

Formula

Recurrence: (n+3)*(3*n-1)*a(n) = (6*n^2+19*n+7)*a(n-1) + 3*(n-1)*(3*n+2)*a(n-2). - Vaclav Kotesovec, Oct 08 2012

a(n) ~ 4*3^(n+1/2)/sqrt(Pi*n). - Vaclav Kotesovec, Oct 08 2012