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 A306644 a(n) = Sum_{k=0..n} (n^2)!/(k! * (n-k)!)^n. 3
 1, 2, 36, 94080, 114144030000, 128569399991042250240, 231970526672859167062880173363200, 974076884952864555606703666490413198470021120000, 13999785014750877128592398884910508842895938385473568105272652000000 (list; graph; refs; listen; history; text; internal format)
 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 Main diagonal of A306641. Sequence in context: A127234 A326961 A181555 * A283261 A280420 A051459 Adjacent sequences: A306641 A306642 A306643 * A306645 A306646 A306647 KEYWORD nonn AUTHOR Seiichi Manyama, Mar 02 2019 STATUS approved

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Last modified March 2 18:02 EST 2024. Contains 370498 sequences. (Running on oeis4.)