A366301 Expansion of e.g.f. 1 / (-5 + Sum_{k=1..6} exp(-k*x)).

1, 21, 791, 44541, 3344327, 313883661, 35351663831, 4645129190541, 697553757742247, 117844709608925901, 22120757207544654071, 4567542244067740041741, 1028853921587420129556167, 251065459281889114259025741, 65978874409961267115296383511, 18577448234544937135538443584141

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1) * binomial(n,k) * (1 + 2^k + ... + 6^k) * a(n-k).

Mathematica

nmax = 15; CoefficientList[Series[1/(-5 + Sum[Exp[-k x], {k, 1, 6}]), {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 + 6^k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 15}]

Crossrefs

Cf. A001553, A004704, A005923, A319509, A366298, A366299, A366300, A366302.

Sequence in context: A220069 A028469 A295845 * A119414 A012819 A297718

Adjacent sequences: A366298 A366299 A366300 * A366302 A366303 A366304

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 06 2023

Status

approved