A277374 a(n) = 2^n*floor(n/2)!*Gamma(ceiling((n+1)/2),-1/4)*exp(-1/4).

1, 2, 3, 6, 50, 100, 1794, 3588, 114840, 229680, 11483880, 22967760, 1653679440, 3307358880, 324121165200, 648242330400, 82975018331520, 165950036663040, 26883905939049600, 53767811878099200, 10753562375623468800, 21507124751246937600, 5204724189801718982400

Offset: 0

Author

Peter Luschny, Oct 17 2016

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..445

Crossrefs

a(n) * A056040(n) = A277393(n).

Programs

Maple

a := n -> 2^n*floor(n/2)!*GAMMA(ceil((n+1)/2),-1/4)*exp(-1/4):
seq(simplify(a(n)),n=0..22);

Mathematica

a[n_] := 2^n Floor[n/2]! Gamma[Ceiling[(1 + n)/2],-1/4] Exp[-1/4];
FunctionExpand@Table[a[n], {n,0,22}]

PARI

for(n=0, 20, print1(round(2^n*(floor(n/2))!*exp(-1/4)* incgam(ceil((n +1)/2), -1/4)), ", ")) \\ G. C. Greubel, May 16 2018

Formula

a(n) ~ Pi*exp(-1/4-n)*n^(n+1) if n is even, a(n) ~ 2*Pi*exp(3/4-n)*(n-1)^n if n is odd. - Vladimir Reshetnikov, Oct 19 2016