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

0,2

Comments

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

Links

Table of n, a(n) for n=0..12.

Example

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

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 *)

Crossrefs

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

Sequence in context: A002555 A239898 A002198 * A163576 A145408 A175672

Adjacent sequences: A276998 A276999 A277000 * A277002 A277003 A277004

Keyword

nonn,frac

Author

Peter Luschny, Sep 25 2016

Status

approved