A087806 Inverse binomial transform of squares of Catalan numbers.

1, 0, 3, 15, 117, 998, 9335, 93054, 974085, 10596336, 118903599, 1368808785, 16099107057, 192831403950, 2346213458667, 28938983482353, 361243476790605, 4557409523980664, 58041112443611015, 745468216328206179, 9647990383169438001, 125732717320525253430

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

G.f.: hypergeom([1/2, 1/2, 1], [2, 2], 16*x/(1+x))/(1+x). E.g.f.: exp(-x)*hypergeom([1/2, 1/2], [2, 2], 16*x).

(n+1)^2*a(n)-(13*n-4)*(n-1)*a(n-1)-(n-1)*(29*n-31)*a(n-2)-15*(n-1)*(n-2)*a(n-3) = 0. - Vladeta Jovovic, Jul 20 2004

a(n) ~ 15^(n+3) / (4096*Pi*n^3). - Vaclav Kotesovec, Oct 30 2017

Mathematica

Table[Sum[(-1)^(n-k) * Binomial[n, k] * CatalanNumber[k]^2, {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Oct 30 2017 *)

Crossrefs

Cf. A007317, A001246, A005043.

Cf. A087804.

Sequence in context: A190629 A341647 A074596 * A245043 A225109 A080290

Adjacent sequences: A087803 A087804 A087805 * A087807 A087808 A087809

Keyword

nonn

Author

Vladeta Jovovic, Oct 12 2003

Extensions

More terms from Vaclav Kotesovec, Oct 30 2017

Status

approved