A373870 a(n) = Sum_{k=1..n} k! * k^(n-3) * |Stirling1(n,k)|.

0, 1, 2, 14, 254, 9154, 552034, 50183832, 6417140232, 1098719459424, 242758470248976, 67260880064331216, 22840933997866565184, 9330599517868641290160, 4514326567036815466609008, 2553018492454631240215801344, 1668797317379516060093446975104

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

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

Prog

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

Crossrefs

Cf. A373869, A373871, A373872.

Cf. A320096, A373855, A373875.

Sequence in context: A219344 A343441 A152476 * A070813 A156214 A370490

Adjacent sequences: A373867 A373868 A373869 * A373871 A373872 A373873

Keyword

nonn

Author

Seiichi Manyama, Jun 20 2024

Status

approved