OFFSET
0,2
FORMULA
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).
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
a(n) = G(n+1)*G(n+3)/G(n+2) for Barnes-G function. - Benedict W. J. Irwin, Jun 21 2018
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
MAPLE
a:=n->mul(denom (k/(k+1)!), k=1..n): seq(a(n), n=0..11); # Zerinvary Lajos, May 31 2008
PROG
(PARI) a(n)=if(n<1, n+1, (n+1)!*prod(k=1, n-1, k!))
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jun 27 2004
STATUS
approved