|
|
A096313
|
|
a(n) = determinant of n X n matrix m(i,j) = Product_{k=1..i} k+j.
|
|
2
|
|
|
1, 2, 6, 48, 1440, 207360, 174182400, 1003290624000, 45509262704640000, 18349334722510848000000, 73244672425152101744640000000, 3189483207556703361731395584000000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
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) ~ 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
|
|
|
STATUS
|
approved
|
|
|
|