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A081051

Stirling numbers of the first kind.

0, 0, 1, -6, 35, -225, 1624, -13132, 118124, -1172700, 12753576, -150917976, 1931559552, -26596717056, 392156797824, -6165817614720, 102992244837120, -1821602444624640, 34012249593822720, -668609730341153280, 13803759753640704000, -298631902863216384000

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OFFSET

0,4

COMMENTS

Coefficient of x^3 in Product {k=0..(n-1), x-k}.

LINKS

Table of n, a(n) for n=0..21.

FORMULA

E.g.f. (1+x)^(-1)*log(1+x)^2/2

a(n) = (-1)^n*det(S(i+3,j+2), 1 <= i,j <= n-2), where S(n,k) are Stirling numbers of the second kind and n>1. [Mircea Merca, Apr 06 2013]

a(n) ~ n! * (-1)^n * log(n)^2/2 * (1 + 2*gamma/log(n)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Mar 03 2022

MATHEMATICA