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

0,2

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

Crossrefs

Cf. A005774.

Sequence in context: A084362 A318941 A079736 * A196859 A090328 A200541

Adjacent sequences: A035042 A035043 A035044 * A035046 A035047 A035048

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved