A366299 Expansion of e.g.f. 1 / (-3 + Sum_{k=1..4} exp(-k*x)).

1, 10, 170, 4300, 145046, 6115900, 309453710, 18267444100, 1232400398966, 93535914320620, 7887919177776350, 731710341934820500, 74046493229735962886, 8117679564133907097340, 958393800813241073719790, 121232569802975799394430500, 16357741845227058108680934806, 2345072789674603792983906178060

Offset

0,2

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1) * binomial(n,k) * (1 + 2^k + 3^k + 4^k) * a(n-k).

Mathematica

nmax = 17; CoefficientList[Series[1/(-3 + Sum[Exp[-k x], {k, 1, 4}]), {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) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 17}]

Crossrefs

Cf. A001551, A004702, A005923, A319509, A366298, A366300, A366301, A366302.

Sequence in context: A120977 A034830 A098345 * A361364 A119043 A187204

Adjacent sequences: A366296 A366297 A366298 * A366300 A366301 A366302

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 06 2023

Status

approved