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%I #22 May 19 2020 09:10:09
%S 1,2,6,48,1440,207360,174182400,1003290624000,45509262704640000,
%T 18349334722510848000000,73244672425152101744640000000,
%U 3189483207556703361731395584000000000
%N a(n) = determinant of n X n matrix m(i,j) = Product_{k=1..i} k+j.
%F a(0)=1, a(1)=2; for n > 1, a(n) = (n+1)!*Product_{k=1..n-1} k!; for n > 1, a(n) = A000142(n+1)*A000178(n-1).
%F G.f.: G(0)/2, where G(k) = 1 + 1/(1 - 1/(1 + 1/((k+1)!+k!)/x/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 14 2013
%F a(n) = G(n+1)*G(n+3)/G(n+2) for Barnes-G function. - _Benedict W. J. Irwin_, Jun 21 2018
%F a(n) ~ n^(n^2/2 + n + 17/12) * (2*Pi)^((n+1)/2) / (A * exp(3*n^2/4 + n - 1/12)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, May 19 2020
%p a:=n->mul(denom (k/(k+1)!), k=1..n): seq(a(n), n=0..11); # _Zerinvary Lajos_, May 31 2008
%o (PARI) a(n)=if(n<1,n+1,(n+1)!*prod(k=1,n-1,k!))
%K nonn
%O 0,2
%A _Benoit Cloitre_, Jun 27 2004
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