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

0,3

Links

Table of n, a(n) for n=0..22.

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A152052 A192661 A020038 * A056845 A354302 A162273

Adjacent sequences: A330013 A330014 A330015 * A330017 A330018 A330019

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 27 2019

Status

approved