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A035045
Inverse binomial transform of A002054.
3
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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved