A347666 E.g.f.: exp( exp(x) * (1 + x + x^2 / 2 + x^3 / 6) - 1 ).

1, 2, 8, 40, 239, 1648, 12778, 109476, 1023520, 10341878, 112067820, 1294254184, 15847382977, 204827368606, 2784056034014, 39665514607872, 590684848605779, 9170941154737032, 148120725648168260, 2483657480026985432, 43157660169344697996, 775898068395820783674

Offset: 0

Author

Ilya Gutkovskiy, Sep 10 2021

Keywords

• nonn

Comments

Exponential transform of A000125.

Crossrefs

Cf. A000125, A001680, A209801, A347665.

Programs

Mathematica

nmax = 21; CoefficientList[Series[Exp[Exp[x] (1 + x + x^2/2 + x^3/6) - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] ((k^3 + 5 k + 6)/6) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A000125(k) * a(n-k).