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A087804
Binomial transform of squares of Catalan numbers.
2
1, 2, 7, 41, 325, 3040, 31515, 350880, 4119125, 50381450, 636749395, 8266178915, 109733663665, 1484513264720, 20411163893039, 284613464884251, 4017787464584397, 57337159218724242, 826192231251644091, 12008313760729689717, 175899654887562881793, 2594832421996070470056, 38524582201629384371391
OFFSET
0,2
LINKS
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)+(-15*n+4+19*n^2)*a(n-1)-(35*n-33)*(n-1)*a(n-2)+17*(n-1)*(n-2)*a(n-3) = 0. - Vladeta Jovovic, Jul 20 2004
a(n) ~ 17^(n+3)/(4096*Pi*n^3). - Vaclav Kotesovec, Oct 14 2012
MATHEMATICA
Table[Sum[Binomial[n, k]*(Binomial[2*k, k]/(k+1))^2, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 14 2012 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(n, k)*(binomial(2*k, k)/(k+1))^2); \\ Joerg Arndt, May 10 2013
CROSSREFS
Cf. A087806.
Sequence in context: A106871 A107376 A220896 * A378325 A006677 A346271
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Oct 12 2003
STATUS
approved