A065236 a(n) = (4*n)!*(n+1)!/(2*n)!.

1, 24, 10080, 15966720, 62270208000, 482718652416000, 6528287055273984000, 141011000393918054400000, 4563680016748763912601600000, 210842016773792892762193920000000

Offset

0,2

Links

Harry J. Smith, Table of n, a(n) for n = 0..50

Formula

Representation as n-th moment of a positive function (expressible in terms of the hypergeometric functions of type 0F2) on a positive half-axis, in Maple notation: a(n)=int(x^n * (1/6720 * (1260 * hypergeom([], [1/2, -3/4], -1/64 * x) * GAMMA(3/4)^2+4 * x^(7/4) * hypergeom([], [9/4, 11/4], -1/64 * x) * sqrt(Pi) * GAMMA(3/4)-105 * sqrt(2) * Pi * hypergeom([], [ -1/4, 3/2], -1/64 * x) * sqrt(x))/Pi^(1/2)/x^(3/4)/GAMMA(3/4)), x=0..infinity), n=0, 1...

Hypergeometric generating function: sum((4 * i)! * (i + 1)! * x^i/((i!)^3 * (2 * i)!), i = 0..infinity) = -1/2 * (-EllipticK(1/2 * sqrt(2) * sqrt((sqrt(1-64 * x)-1)/(1-64 * x)^(1/2))) + 3 * sqrt(1-64 * x) * EllipticK(1/2 * sqrt(2) * sqrt((sqrt(1-64 * x)-1)/(1-64 * x)^(1/2))) + 2 * EllipticE(1/2 * sqrt(2) * sqrt((sqrt(1-64 * x)-1)/(1-64 * x)^(1/2)))) * (1-64 * x)^(1/4)/(64 * x-1)/Pi

Mathematica

Table[((4n)!(n+1)!)/(2n)!, {n, 0, 10}] (* Harvey P. Dale, Jan 26 2014 *)

Prog

(PARI) { for (n=0, 50, write("b065236.txt", n, " ", (4*n)!*(n + 1)!/(2*n)!) ) } \\ Harry J. Smith, Oct 14 2009

Crossrefs

Sequence in context: A233148 A195681 A239166 * A074657 A208190 A338527

Adjacent sequences: A065233 A065234 A065235 * A065237 A065238 A065239

Keyword

nonn

Author

Karol A. Penson, Oct 23 2001

Status

approved