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A087806
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Inverse binomial transform of squares of Catalan numbers.
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1
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1, 0, 3, 15, 117, 998, 9335, 93054, 974085, 10596336, 118903599, 1368808785, 16099107057, 192831403950, 2346213458667, 28938983482353, 361243476790605, 4557409523980664, 58041112443611015, 745468216328206179, 9647990383169438001, 125732717320525253430
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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MATHEMATICA
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Table[Sum[(-1)^(n-k) * Binomial[n, k] * CatalanNumber[k]^2, {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Oct 30 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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