A337555 a(0) = 1; a(n) = (1/2) * Sum_{k=1..n} binomial(n,k) * (3^k-1) * a(n-k).

1, 1, 6, 43, 408, 4861, 69516, 1159663, 22108848, 474192601, 11300589876, 296237533483, 8471642214888, 262456441714741, 8756520140416236, 313017838828154503, 11935355244756882528, 483537933291091103281, 20741938090482567562596, 939180816648348685174723

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

E.g.f.: 2 / (2 + exp(x) - exp(3*x)).

a(n) ~ n! / ((r+3) * log(r)^(n+1)), where r = 1.52137970680456756960408... is the real root of the equation r^3 - r = 2. - Vaclav Kotesovec, Aug 31 2020

Mathematica

a[0] = 1; a[n_] := a[n] = (1/2) Sum[Binomial[n, k] (3^k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
nmax = 19; CoefficientList[Series[2/(2 + Exp[x] - Exp[3 x]), {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) seq(n)={Vec(serlaplace(2 / (2 + exp(x + O(x*x^n)) - exp(3*x + O(x*x^n)))))} \\ Andrew Howroyd, Aug 31 2020

Crossrefs

Cf. A000556, A003462, A337556.

Sequence in context: A176732 A062266 A217485 * A290783 A159604 A090338

Adjacent sequences: A337552 A337553 A337554 * A337556 A337557 A337558

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 31 2020

Status

approved