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A328182 Expansion of e.g.f. 1 / (2 - exp(3*x)). 3
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

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

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

Cf. A000670, A216794, A247452, A328183.

Sequence in context: A067000 A307650 A168593 * A157089 A138436 A141057

Adjacent sequences:  A328179 A328180 A328181 * A328183 A328184 A328185

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 06 2019

STATUS

approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)