A366300 Expansion of e.g.f. 1 / (-4 + Sum_{k=1..5} exp(-k*x)).

1, 15, 395, 15525, 813671, 53306325, 4190730335, 384368222925, 40289992211591, 4751157347330085, 622528350091484975, 89724601853904952125, 14107579506569655343511, 2403010007367884873188245, 440801776092151383251034815, 86635186648455606881413582125, 18162432724968339044562784395431

Offset: 0

Author

Ilya Gutkovskiy, Oct 06 2023

Keywords

• nonn

Crossrefs

Cf. A001552, A004703, A005923, A319509, A366298, A366299, A366301, A366302.

Programs

Mathematica

nmax = 16; CoefficientList[Series[1/(-4 + Sum[Exp[-k x], {k, 1, 5}]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) Binomial[n, k] (1 + 2^k + 3^k + 4^k + 5^k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 16}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1) * binomial(n,k) * (1 + 2^k + ... + 5^k) * a(n-k).