A371624 - OEIS

A371624

a(n) = Product_{k=0..n} (n^2 - k^2)!.

1, 1, 144, 1755758592000, 66052111513207347990207922176000000000

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OFFSET

0,3

COMMENTS

The next term has 88 digits.

LINKS

Table of n, a(n) for n=0..4.

FORMULA

a(n) = (n^2)!^(n+1) / (A255322(n) * A371603(n)).

a(n) ~ c * A^(2*n) * 2^(4*n*(n^2 + 1)/3) * Pi^(n/2) * n^(4*n^3/3 + n^2 + 5*n/6 + 1/4) / exp(16*n^3/9 + n^2/2 + n), where c = 1.291409... = sqrt(2*Pi) / (A255504 * c from A371603) and A is the Glaisher-Kinkelin constant A074962.

MATHEMATICA

Table[Product[((2*n-k)*k)!, {k, 0, n}], {n, 0, 6}]

Table[Product[(n^2 - k^2)!, {k, 0, n}], {n, 0, 6}]

CROSSREFS

Cf. A001142, A255322, A296591, A362288, A371603.

Sequence in context: A193346 A003837 A013863 * A173225 A126843 A099648

Adjacent sequences: A371621 A371622 A371623 * A371625 A371626 A371627

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 30 2024

STATUS

approved