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A366298
Expansion of e.g.f. 1 / (-2 + Sum_{k=1..3} exp(-k*x)).
4
1, 6, 58, 828, 15766, 375276, 10719118, 357202068, 13603819126, 582854637276, 27747071520478, 1453003753611108, 83005119616449286, 5136947527401250476, 342365553703113120238, 24447711909762202272948, 1862151878019906517540246, 150702660087903415402794876, 12913688931657425188926182398
OFFSET
0,2
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}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 06 2023
STATUS
approved