A354686 a(n) = n! * Sum_{k=1..n} Stirling1(n,k) * H(k), where H(k) is the k-th harmonic number.

0, 1, 1, -4, 38, -646, 17124, -651120, 33563760, -2251415376, 190506294720, -19843054116480, 2494435702953600, -372324067662349440, 65089674982557308160, -13172994619821785548800, 3055455516855073351219200, -805168341051328705189939200

Offset

0,4

Links

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

Formula

Sum_{n>=0} a(n) * x^n / n!^2 = Sum_{n>=1} H(n) * log(1+x)^n / n!.

Mathematica

Table[n! Sum[StirlingS1[n, k] HarmonicNumber[k], {k, 1, n}], {n, 0, 17}]
nmax = 17; CoefficientList[Series[Sum[HarmonicNumber[k] Log[1 + x]^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^2

Crossrefs

Cf. A001008, A002805, A087751, A222059, A302547, A354685.

Sequence in context: A138214 A195442 A138562 * A177382 A201861 A171779

Adjacent sequences: A354683 A354684 A354685 * A354687 A354688 A354689

Keyword

sign

Author

Ilya Gutkovskiy, Jun 03 2022

Status

approved