A385752 a(n) = Sum_{k=0..n} Stirling1(n,k) * (n!/k!)^2.

1, 1, -3, 46, -1967, 179351, -29861639, 8200834972, -3456505906559, 2118756407303197, -1811589861406160699, 2089746219541021377546, -3164800617505630505525903, 6151223064132377579849537011, -15052264342298428131766095419839, 45616620088948927404807879986431576, -168785206495071742797011703980958673919

Offset: 0

Author

Ilya Gutkovskiy, Jul 08 2025

Keywords

• sign

Crossrefs

Cf. A119391, A192554, A385750, A385751.

Programs

Mathematica

Table[Sum[StirlingS1[n, k] (n!/k!)^2, {k, 0, n}], {n, 0, 16}]
nmax = 16; CoefficientList[Series[Sum[Log[1 + x]^k/k!^3, {k, 0, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^3

Formula

Sum_{n>=0} a(n) * x^n / n!^3 = Sum_{k>=0} log(1 + x)^k / k!^3.