OFFSET
0,4
COMMENTS
Coefficient of x^3 in Product {k=0..(n-1), x-k}.
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
Table[StirlingS1[n, 3], {n, 1, 20}] (* Vaclav Kotesovec, Mar 03 2022 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Mar 05 2003
STATUS
approved