A337552 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (3*k-2) * a(n-k).
1, 1, 6, 37, 330, 3613, 47652, 732625, 12875118, 254540413, 5591435136, 135108218353, 3561467337546, 101704047315037, 3127751183515020, 103059820083026449, 3622223857996975110, 135266462416766669917, 5348457650664454581240, 223227700948792985989777
Offset: 0
Keywords
Programs
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Mathematica
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (3 k - 2) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}] nmax = 19; CoefficientList[Series[1/(Exp[x] (2 - 3 x) - 1), {x, 0, nmax}], x] Range[0, nmax]! -
PARI
seq(n)={Vec(serlaplace(1 / (exp(x + O(x*x^n)) * (2 - 3*x) - 1)))} \\ Andrew Howroyd, Aug 31 2020
Formula
E.g.f.: 1 / (exp(x) * (2 - 3*x) - 1).
a(n) ~ n! * c / ((1-c) * (2/3 - c)^(n+1)), where c = -LambertW(-exp(-2/3)/3). - Vaclav Kotesovec, Aug 31 2020