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A272168 a(n) = Product_{k=0..n} (k^2-k)!. 2
1, 1, 2, 1440, 689762304000, 1678124094566146045378560000000, 445127215203413988036981576746329306509322538188800000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The next term has 114 digits.

LINKS

Table of n, a(n) for n=0..6.

FORMULA

a(n) ~ c * n^(n*(2*n^2 + 1)/3) * (2*Pi)^(n/2) / exp(5*n^3/9 + n/2 - Zeta(3) / (2*Pi^2)), where c = Product_{k>=2} (k*(k-1))!/stirling(k*(k-1)) = 1.086533635964823338078329042... and stirling(n) = sqrt(2*Pi*n) * n^n / exp(n) is the Stirling approximation of n!.

MATHEMATICA

Table[Product[(k^2-k)!, {k, 0, n}], {n, 0, 8}]

CROSSREFS

Cf. A272094, A272167.

Sequence in context: A157494 A227247 A294321 * A173131 A160087 A170993

Adjacent sequences:  A272165 A272166 A272167 * A272169 A272170 A272171

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Apr 21 2016

STATUS

approved

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Last modified September 19 12:17 EDT 2020. Contains 337178 sequences. (Running on oeis4.)