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%I #14 Sep 09 2018 09:40:07
%S 1,24,5760,2903040,1393459200,367873228800,24103053950976000,
%T 115694658964684800,9440684171518279680000,
%U 271211974879377138647040000,3579998068407778230140928000000,1976158933761093583037792256000000,258955866680053703121272297226240000000
%N Denominators of an asymptotic series for the Gamma function (even power series).
%C For formulas and references see A277000 which is the main entry for this rational sequence.
%e The underlying rational sequence starts:
%e 1, 0, -1/24, 0, 19/5760, 0, -2561/2903040, 0, 874831/1393459200, 0, ...
%p b := n -> CompleteBellB(n,0,seq((k-2)!*bernoulli(k,1/2),k=2..n))/n!:
%p A277001 := n -> denom(b(2*n)): seq(A277001(n), n=0..12);
%t CompleteBellB[n_, zz_] := Sum[BellY[n, k, zz[[1 ;; n-k+1]]], {k, 1, n}];
%t b[n_] := CompleteBellB[n, Join[{0}, Table[(k-2)! BernoulliB[k, 1/2], {k, 2, n}]]]/n!;
%t a[n_] := Denominator[b[2n]];
%t Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, Sep 09 2018 *)
%Y Cf. A277000 (numerators), A277002/A277003 (odd power series).
%K nonn,frac
%O 0,2
%A _Peter Luschny_, Sep 25 2016
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