A336210 a(0) = 1; a(n) = -(1/n) * Sum_{k=0..n-1} binomial(n,k)^3 * (n-k) * a(k).

1, -1, 3, -10, -117, 5224, -23010, -10319891, 463834315, 69461529092, -10005601418172, -1323175060249241, 468450359815048182, 63281374513705043227, -46495538420749056681263, -7147072328212024308730535, 9119277358213513566069911755, 1827085356172328516064256064092

Offset: 0

Author

Ilya Gutkovskiy, Jul 12 2020

Keywords

• sign

Crossrefs

Cf. A000587, A061684, A336209.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = -(1/n) Sum[Binomial[n, k]^3 (n - k) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 17}]
nmax = 17; CoefficientList[Series[Exp[-Sum[x^k/(k!)^3, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^3

Formula

a(n) = (n!)^3 * [x^n] exp(-Sum_{k>=1} x^k / (k!)^3).