A096313 a(n) = determinant of n X n matrix m(i,j) = Product_{k=1..i} k+j.

1, 2, 6, 48, 1440, 207360, 174182400, 1003290624000, 45509262704640000, 18349334722510848000000, 73244672425152101744640000000, 3189483207556703361731395584000000000

Offset

0,2

Links

Table of n, a(n) for n=0..11.

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

Sequence in context: A275462 A063744 A141609 * A346788 A230053 A245283

Adjacent sequences: A096310 A096311 A096312 * A096314 A096315 A096316

Keyword

nonn

Author

Benoit Cloitre, Jun 27 2004

Status

approved