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A328182 Expansion of e.g.f. 1 / (2 - exp(3*x)). 7
1, 3, 27, 351, 6075, 131463, 3413907, 103429791, 3581223435, 139498558263, 6037616347587, 287444492409231, 14929010774254395, 839982382565841063, 50897213545996785267, 3304312091004451756671, 228821504027595115886955, 16836102104577636004291863, 1311625494765417347634022947 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} 3^k * binomial(n,k) * a(n-k).
a(n) = Sum_{k>=0} (3*k)^n / 2^(k + 1).
a(n) = 3^n * A000670(n).
a(n) ~ n! * 3^n / (2 * log(2)^(n+1)). - Vaclav Kotesovec, Aug 09 2021
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-j)*binomial(n, j)*3^j, j=1..n))
end:
seq(a(n), n=0..20); # Alois P. Heinz, Oct 06 2019
MATHEMATICA
nmax = 18; CoefficientList[Series[1/(2 - Exp[3 x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[3^k Binomial[n, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
Table[3^n HurwitzLerchPhi[1/2, -n, 0]/2, {n, 0, 18}]
CROSSREFS
Sequence in context: A307650 A168593 A364431 * A372201 A370288 A157089
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 06 2019
STATUS
approved

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Last modified June 15 19:43 EDT 2024. Contains 373410 sequences. (Running on oeis4.)