OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..345
FORMULA
a(n) = ((2*n)!/n!) * [x^(2*n)] log(1 - log(1 - x))^n.
a(n) ~ c * d^n * (n-1)!, where d = 5.87606029984908... and c = 0.08380514489... - Vaclav Kotesovec, Feb 17 2021
MATHEMATICA
Table[Sum[Abs[StirlingS1[2 n, k]] StirlingS1[k, n], {k, n, 2 n}], {n, 0, 18}]
Table[((2 n)!/n!) SeriesCoefficient[Log[1 - Log[1 - x]]^n, {x, 0, 2 n}], {n, 0, 18}]
PROG
(PARI) a(n) = sum(k=n, 2*n, abs(stirling(2*n, k, 1))*stirling(k, n, 1)); \\ Michel Marcus, Feb 16 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 15 2021
STATUS
approved