A373872 a(n) = Sum_{k=1..n} (-1)^(n-k) * k! * k^(n-3) * Stirling2(n,k).

0, 1, 0, 1, 15, 391, 16275, 999391, 85314915, 9682617631, 1411532175075, 257220473522431, 57317980108103715, 15338554965273810271, 4855172557420679314275, 1794588990417909081447871, 766066194581899382513514915, 374061220058388896558805473311

Offset

0,5

Links

Table of n, a(n) for n=0..17.

Formula

E.g.f.: Sum_{k>=1} (1 - exp(-k*x))^k / k^3.

Sum_{k>=0} a(k+2) * x^k/k!　= Sum_{k>=0} k * (1 - exp(-k*x))^k.

Prog

(PARI) a(n) = sum(k=1, n, (-1)^(n-k)*k!*k^(n-3)*stirling(n, k, 2));

Crossrefs

Cf. A373869, A373870, A373871.

Cf. A092552, A220181.

Sequence in context: A069990 A157581 A143001 * A250950 A366300 A323838

Adjacent sequences: A373869 A373870 A373871 * A373873 A373874 A373875

Keyword

nonn

Author

Seiichi Manyama, Jun 20 2024

Status

approved