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A087806 Inverse binomial transform of squares of Catalan numbers. 1
1, 0, 3, 15, 117, 998, 9335, 93054, 974085, 10596336, 118903599, 1368808785, 16099107057, 192831403950, 2346213458667, 28938983482353, 361243476790605, 4557409523980664, 58041112443611015, 745468216328206179, 9647990383169438001, 125732717320525253430 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 16:58 EST 2022. Contains 358588 sequences. (Running on oeis4.)