A343709 a(n) = 1 + 3 * Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).

1, 4, 28, 295, 4159, 73348, 1552468, 38336569, 1081926157, 34350646636, 1211796777748, 47023762576987, 1990643657768683, 91291802205304972, 4508735102829489580, 238583762726054522989, 13466532093135977880025, 807606110028529741369396, 51282242176105846536128236

Offset: 0

Author

Ilya Gutkovskiy, Apr 26 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..371

Crossrefs

Cf. A201354, A291979, A343707, A343710.

Programs

Mathematica

a[n_] := a[n] = 1 + 3 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 + 3 Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!

PARI

N=20; x='x+O('x^N); Vec(serlaplace(exp(x)/(1+3*log(1-x)))) \\ Seiichi Manyama, Oct 20 2021

Formula

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