A341598 a(n) = Sum_{k=n..2*n} |Stirling1(2*n, k)| * Stirling1(k, n).

1, 0, 4, 15, 728, 9660, 454333, 11921910, 620800752, 25052417676, 1495629968820, 81260657073596, 5594820193907943, 379090865741895580, 29938401724408721880, 2414113646907092768775, 216602054576835471646080, 20165486015516015341186800, 2034029167741961519973600460

Offset: 0

Author

Ilya Gutkovskiy, Feb 15 2021

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..345

Crossrefs

Cf. A008275, A079642, A089064, A321712, A341575, A341589.

Programs

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}]

PARI

a(n) = sum(k=n, 2*n, abs(stirling(2*n, k, 1))*stirling(k, n, 1)); \\ Michel Marcus, Feb 16 2021

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