A366302 Expansion of e.g.f. 1 / (-6 + Sum_{k=1..7} exp(-k*x)).

1, 28, 1428, 108976, 11088924, 1410452848, 215282610348, 38335940184976, 7801807561068444, 1786227911508713008, 454397569178386774668, 127153351764004535348176, 38815768300684586111354364, 12836619471891836987050169968, 4571701128215207034965181098988, 1744488930796462320024115801858576

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 + ... + 7^k) * a(n-k).

Mathematica

nmax = 15; CoefficientList[Series[1/(-6 + Sum[Exp[-k x], {k, 1, 7}]), {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 + 7^k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 15}]

Crossrefs

Cf. A001554, A004705, A005923, A319509, A366298, A366299, A366300, A366301.

Sequence in context: A213692 A118705 A249348 * A013926 A110696 A007222

Adjacent sequences: A366299 A366300 A366301 * A366303 A366304 A366305

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 06 2023

Status

approved