OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..24
FORMULA
a(n) ~ c * 2^(n^2 + 1/2) * n^(n^2 - n + 1) / Pi^(n - 1/2), where c = exp(-1/3)*JacobiTheta3(0, exp(-2)) = exp(-1/3) * EllipticTheta[3, 0, exp(-2)] = 0.910956007080971245990320395256172663671471380838524358269586617628532... if n is even and c = exp(-1/3) * JacobiTheta2(0, exp(-2)) = exp(-1/3) * EllipticTheta[3, 0, exp(-2)] = 0.885121645271745566745223804647879414416684832686710775956467801722557... if n is odd. - Vaclav Kotesovec, Jun 21 2021
MATHEMATICA
a[n_] := Sum[(n^2)!/(k! * (n-k)!)^n, {k, 0, n}]; Array[a, 9, 0] (* Amiram Eldar, Jun 21 2021 *)
PROG
(PARI) {a(n) = sum(k=0, n, (n^2)!/(k!*(n-k)!)^n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 02 2019
STATUS
approved