A373857 a(n) = Sum_{k=1..n} k! * k^(n-1) * Stirling1(n,k).

0, 1, 3, 32, 734, 28994, 1752046, 150262104, 17356844088, 2597710341600, 488957612319984, 113044488306692304, 31490845086661001664, 10403092187976909854640, 4021236906890850070201488, 1798052050351216209712206336, 920859156623446912386646303104

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.

Mathematica

nmax=16; Range[0, nmax]!CoefficientList[Series[Sum[(Log[1 + k*x])^k / k, {k, nmax}], {x, 0, nmax}], x] (* Stefano Spezia, Jun 19 2024 *)

Prog

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

Crossrefs

Cf. A092552, A244585, A373855.

Cf. A320082, A320083.

Sequence in context: A295385 A331799 A129431 * A297558 A283716 A373875

Adjacent sequences: A373854 A373855 A373856 * A373858 A373859 A373860

Keyword

nonn

Author

Seiichi Manyama, Jun 19 2024

Status

approved