A264152 a(n) = (2^floor(n+n/2)/sqrt(Pi)^mod(n+1,2))*Gamma(n+1/2)/Gamma(n/2+1).

1, 2, 6, 40, 210, 2016, 13860, 164736, 1351350, 18670080, 174594420, 2708858880, 28109701620, 479259648000, 5421156741000, 100069414502400, 1218404977539750, 24087296714342400, 312723944235202500, 6566957735804928000, 90252130306279441500, 2000107698962300928000

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..565

Formula

a(n) = A001813(n)/A006882(n).

a(n) = A000079(n)*A006882(2*n-1)/A006882(n).

E.g.f.: 2F2(1/4,3/4;1/2,1;8*x^2) + 2*x*2F2(3/4,5/4;3/2,3/2;8*x^2). - Benedict W. J. Irwin, Aug 15 2016

a(n) ~ 2^(2*n) * n^((n-1)/2) * exp(-n/2) * (2/Pi)^((1+(-1)^n)/4). - Ilya Gutkovskiy, Aug 15 2016

Maple

a := n -> (2^floor(n+n/2)/sqrt(Pi)^modp(n+1, 2))*GAMMA(n+1/2)/GAMMA(n/2+1):
seq(a(n), n=0..21);

Mathematica

Table[CoefficientList[Series[HypergeometricPFQ[{1/4, 3/4}, {1/2, 1}, 8 x^2] +
2 x HypergeometricPFQ[{3/4, 5/4}, {3/2, 3/2}, 8 x^2], {x, 0, 20}], x][[n]] (n - 1)!, {n, 1, 20}] (* Benedict W. J. Irwin, Aug 15 2016 *)
Table[(2^Floor[n + n/2]/Sqrt[Pi]^Mod[n + 1, 2])*Gamma[n + 1/2]/Gamma[n/2 + 1], {n, 0, 20}] (* Benedict W. J. Irwin, Aug 15 2016 *)

Prog

(Sage)
a = lambda n: (rising_factorial(1/2, n) // n.multifactorial(2)) << 2*n
[a(n) for n in (0..21)]

Crossrefs

Cf. A000079, A001813, A006882.

Sequence in context: A081096 A350971 A119692 * A333631 A337071 A354313

Adjacent sequences: A264149 A264150 A264151 * A264153 A264154 A264155

Keyword

nonn

Author

Peter Luschny, Nov 06 2015

Status

approved