A277001 Denominators of an asymptotic series for the Gamma function (even power series).

1, 24, 5760, 2903040, 1393459200, 367873228800, 24103053950976000, 115694658964684800, 9440684171518279680000, 271211974879377138647040000, 3579998068407778230140928000000, 1976158933761093583037792256000000, 258955866680053703121272297226240000000

Offset: 0

Author

Peter Luschny, Sep 25 2016

Keywords

• nonn
• frac

Comments

For formulas and references see A277000 which is the main entry for this rational sequence.

Examples

			The underlying rational sequence starts:
1, 0, -1/24, 0, 19/5760, 0, -2561/2903040, 0, 874831/1393459200, 0, ...
		

Crossrefs

Cf. A277000 (numerators), A277002/A277003 (odd power series).

Programs

Maple

b := n -> CompleteBellB(n,0,seq((k-2)!*bernoulli(k,1/2),k=2..n))/n!:
A277001 := n -> denom(b(2*n)): seq(A277001(n), n=0..12);

Mathematica

CompleteBellB[n_, zz_] := Sum[BellY[n, k, zz[[1 ;; n-k+1]]], {k, 1, n}];
b[n_] := CompleteBellB[n, Join[{0}, Table[(k-2)! BernoulliB[k, 1/2], {k, 2, n}]]]/n!;
a[n_] := Denominator[b[2n]];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Sep 09 2018 *)