A330016 a(n) = Sum_{k=1..n} (-1)^(n - k) * H(k) * k!, where H(k) is the k-th harmonic number.

0, 1, 2, 9, 41, 233, 1531, 11537, 98047, 928529, 9700111, 110843729, 1375599151, 18427159889, 265038487471, 4074124514129, 66660157879471, 1156745432699729, 21220242625821871, 410344904191816529, 8342603132569783471, 177902207647600456529, 3970574571687854263471

Offset: 0

Author

Ilya Gutkovskiy, Nov 27 2019

Keywords

• nonn

Crossrefs

Cf. A000254, A001008, A002805, A092692, A097422.

Programs

Mathematica

Table[Sum[(-1)^(n - k) HarmonicNumber[k] k!, {k, 1, n}], {n, 0, 22}]

Formula

a(n) = Sum_{k=1..n} (-1)^(n - k) * |Stirling1(k+1,2)|.