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A324590 a(n) = n!^(4*n) * Product_{k=1..n} binomial(n + 1/k^2, n). 2
2, 1080, 16133644800, 139256878046022696960000, 6288402750181849898716908922601472000000000, 8322157105451357856813375261666887975745751468393837363200000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..6.

FORMULA

a(n) ~ n!^(4*n) * n^(Pi^2/6) / A303670.

a(n) ~ n^(4*n^2 + 2*n + Pi^2/6) * (2*Pi)^(2*n) / exp(4*n^2 - 1/3 - 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.

a(n) = n!^n * A324596(n).

MATHEMATICA

Table[n!^(4*n) * Product[Binomial[1/k^2 + n, n], {k, 1, n}], {n, 1, 8}]

CROSSREFS

Cf. A303670, A306760, A306774, A324589.

Sequence in context: A159858 A108963 A152510 * A344669 A321633 A244550

Adjacent sequences:  A324587 A324588 A324589 * A324591 A324592 A324593

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 09 2019

STATUS

approved

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Last modified January 16 16:17 EST 2022. Contains 350376 sequences. (Running on oeis4.)