A336951 E.g.f.: 1 / (1 - x * exp(3*x)).

1, 1, 8, 69, 780, 11145, 191178, 3823785, 87406056, 2247785073, 64228084110, 2018771719569, 69221032558956, 2571290056399545, 102860527370221026, 4408690840306136505, 201557641172689004112, 9790792086366911655009, 503570143277542340304534

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..383

Formula

a(n) = n! * Sum_{k=0..n} (3 * (n-k))^k / k!.

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

a(n) ~ n! * (3/LambertW(3))^n / (1 + LambertW(3)). - Vaclav Kotesovec, Aug 09 2021

Mathematica

nmax = 18; CoefficientList[Series[1/(1 - x Exp[3 x]), {x, 0, nmax}], x] Range[0, nmax]!
Join[{1}, Table[n! Sum[(3 (n - k))^k/k!, {k, 0, n}], {n, 1, 18}]]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] k 3^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]

Prog

(PARI) seq(n)={ Vec(serlaplace(1 / (1 - x*exp(3*x + O(x^n))))) } \\ Andrew Howroyd, Aug 08 2020

Crossrefs

Column k=3 of A351790.

Cf. A006153, A027471, A235328, A255927, A328182, A336948, A336950, A336952.

Sequence in context: A222064 A317096 A327606 * A335114 A226597 A376855

Adjacent sequences: A336948 A336949 A336950 * A336952 A336953 A336954

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 08 2020

Status

approved