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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

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OFFSET

0,2

LINKS

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

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

MATHEMATICA

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

PROG

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