A033542 a(n) = 2*(n^2)!* Product_{k = 1..n-1} k!/(n+k)!.

0, 2, 8, 504, 1153152, 168275764800, 2407165968578342400, 4788742737385049982623884800, 1780642079411485280163076498360356864000, 159943989198524502594920793284078996733117111490560000, 4353607386405822605116660595502838129080647848043621660449907712000000

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..29

Formula

a(n) ~ Pi * exp(n^2/2 - n + 1/12) * n^(n^2 + n + 17/12) / (A * 2^(2*n^2 - 25/12)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Oct 15 2019

Maple

seq(`if`(n=0, 0, 2*factorial(n^2)*mul(factorial(k)/factorial(n+k), k = 1 .. n-1)), n = 0..10); # G. C. Greubel, Oct 12 2019

Mathematica

Table[If[n==0, 0, 2*(n^2)!*Product[k!/(n+k)!, {k, 1, n-1}]], {n, 0, 10}] (* G. C. Greubel, Oct 12 2019 *)
Flatten[{0, Table[2*BarnesG[n+1]*BarnesG[n+2]*(n^2)!/BarnesG[2*n + 1], {n, 1, 10}]}] (* Vaclav Kotesovec, Oct 15 2019 *)

Prog

(PARI) concat([0], vector(10, n, 2*(n^2)!*prod(k=1, n-1, k!/(n+k)!) )) \\ G. C. Greubel, Oct 12 2019
(Magma) [0, 2] cat [2*Factorial(n^2)*(&*[Factorial(k)/Factorial(n+k): k in [1..n-1]]): n in [2..10]]; // G. C. Greubel, Oct 12 2019
(Sage) [0]+[2*factorial(n^2)*product(factorial(k)/factorial(n+k) for k in (1..n-1)) for n in (1..10)] # G. C. Greubel, Oct 12 2019
(GAP) Concatenation([0], List([1..10], n-> 2*Factorial(n^2)*Product([1..n-1], k-> Factorial(k)/Factorial(n+k)) )); # G. C. Greubel, Oct 12 2019

Crossrefs

Sequence in context: A323863 A003301 A000890 * A098870 A221065 A023365

Adjacent sequences: A033539 A033540 A033541 * A033543 A033544 A033545

Keyword

nonn

Author

Robert G. Wilson v, Feb 13 2002

Extensions

Definition corrected by Neven Juric, Nov 08 2012

Status

approved