A343710 a(n) = 1 + 4 * Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).

1, 5, 45, 609, 11009, 248837, 6749629, 213596401, 7725031521, 314310704101, 14209394894765, 706617979262049, 38333841625642785, 2252901018519028901, 142589176837851349757, 9669282207517755852721, 699408060608904410296897, 53752166013267632536864581, 4374061543586452325644329133

Offset: 0

Author

Ilya Gutkovskiy, Apr 26 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..359

Crossrefs

Cf. A201365, A291979, A343707, A343709.

Programs

Mathematica

a[n_] := a[n] = 1 + 4 Sum[Binomial[n, k] (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[x]/(1 + 4 Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!

PARI

N=20; x='x+O('x^N); Vec(serlaplace(exp(x)/(1+4*log(1-x)))) \\ Seiichi Manyama, Oct 20 2021

Formula

E.g.f.: exp(x) / (1 + 4 * log(1 - x)).