A103207 a(n)=(-1)^floor(n/2)/det(M_n) where M_n is the n X n matrix of terms 1/(i+j)! i and j ranging from 1 to n.

1, 2, 144, 1036800, 1463132160000, 668986161758208000000, 148045794139338685651353600000000, 22147346968743318573346465338485637120000000000

Offset

0,2

Links

Table of n, a(n) for n=0..7.

Formula

a(n)=(1/2^n)*{prod(k=1, n, (2*k)!/k!)}^2.

a(n) ~ A * 2^(2*n^2 + 2*n + 5/12) * n^(n^2 + n + 1/12) / exp(3*n^2/2 + n + 1/12), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, May 01 2015

Maple

seq(mul(mul(k+j, j=1..n), k=0..n), n=0..7); # Zerinvary Lajos, Jun 01 2007

Mathematica

Table[1/2^n*(Product[(2*k)!/k!, {k, 1, n}])^2, {n, 0, 10}] (* Vaclav Kotesovec, May 01 2015 *)
Table[2^(2*n^2 + n - 1/12) * Glaisher^3 * BarnesG[n+3/2]^2 / (E^(1/4) * Pi^(n+1/2)), {n, 0, 10}] (* Vaclav Kotesovec, May 01 2015 *)

Prog

(PARI) a(n)=(1/2^n)*prod(k=1, n, (2*k)!/k!)^2

Crossrefs

Cf. A062381.

Sequence in context: A304461 A264153 A232998 * A093002 A074319 A188284

Adjacent sequences: A103204 A103205 A103206 * A103208 A103209 A103210

Keyword

nonn

Author

Benoit Cloitre, Mar 19 2005

Status

approved