A366298 Expansion of e.g.f. 1 / (-2 + Sum_{k=1..3} exp(-k*x)).

1, 6, 58, 828, 15766, 375276, 10719118, 357202068, 13603819126, 582854637276, 27747071520478, 1453003753611108, 83005119616449286, 5136947527401250476, 342365553703113120238, 24447711909762202272948, 1862151878019906517540246, 150702660087903415402794876, 12913688931657425188926182398

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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

Mathematica

nmax = 18; CoefficientList[Series[1/(-2 + Sum[Exp[-k x], {k, 1, 3}]), {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) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]

Crossrefs

Cf. A001550, A004701, A005923, A319509, A366299, A366300, A366301, A366302.

Sequence in context: A302598 A302922 A370908 * A337594 A274985 A034982

Adjacent sequences: A366295 A366296 A366297 * A366299 A366300 A366301

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 06 2023

Status

approved