A372803 Expansion of e.g.f. exp(1 - exp(-x)) * (exp(-x) - 1) * (exp(-x) - 2).

0, 1, 3, -2, -11, 31, 14, -349, 1047, 820, -21265, 90355, -26352, -2086083, 14092615, -32449650, -241320287, 3080629195, -15455723498, -2456654665, 760213889483, -7097893818852, 28459679925187, 125560349169887, -3153253543188992, 26852335900600041, -86130449768002245

Offset: 0

Author

Ilya Gutkovskiy, May 14 2024

Keywords

• sign

Crossrefs

Cf. A000587, A033452, A045406, A101851, A151881.

Programs

Mathematica

nmax = 26; CoefficientList[Series[Exp[1 - Exp[-x]] (Exp[-x] - 1) (Exp[-x] - 2), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^(n - k) StirlingS2[n, k] k^2, {k, 0, n}], {n, 0, 26}]

Formula

G.f.: Sum_{k>=0} k^2 * x^k / Product_{j=0..k} (1 + j*x).

a(n) = Sum_{k=0..n} (-1)^(n-k) * Stirling2(n,k) * k^2.