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A324596 a(n) = n!^(3*n) * Product_{k=1..n} binomial(n + 1/k^2, n). 2
2, 270, 74692800, 419731620267960000, 252716802910471719823692648960000, 59736659298524125157504488525739821430187940800000000, 16079377413231597423103950774423398920424350187193326745026311068057600000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..7.

FORMULA

a(n) ~ n!^(3*n) * n^(Pi^2/6) / A303670.

a(n) ~ n^(3*n*(2*n+1)/2 + Pi^2/6) * (2*Pi)^(3*n/2) / exp(3*n^2 - 1/4 - gamma*Pi^2/6 + c), where gamma is the Euler-Mascheroni constant A001620 and c = A306774 = Sum_{k>=2} (-1)^k * Zeta(k) * Zeta(2*k) / k.

MATHEMATICA

Table[n!^(3*n) * Product[Binomial[n + 1/k^2, n], {k, 1, n}], {n, 1, 8}]

CROSSREFS

Cf. A303670, A306760, A306774, A324589, A324597.

Sequence in context: A188964 A278771 A318171 * A007512 A048534 A135696

Adjacent sequences:  A324588 A324589 A324590 * A324597 A324609 A324610

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 09 2019

STATUS

approved

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Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)