A347435 E.g.f.: exp( exp(x) * (exp(x) - 1 - x - x^2 / 2 - x^3 / 6) ).

1, 0, 0, 0, 1, 6, 22, 64, 198, 1138, 10004, 83920, 617993, 4226028, 30103686, 251883012, 2490287821, 26456763078, 281404300348, 2966101610920, 31877462564554, 362624252399566, 4437794875670072, 57612897938229380, 773900876490016325, 10599854900351622752

Offset

0,6

Comments

Exponential transform of A002663.

Links

Table of n, a(n) for n=0..25.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002663(k) * a(n-k).

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-j)*binomial(n-1, j-1)*(2^j-j^3/6-5*j/6-1), j=1..n))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Sep 02 2021

Mathematica

nmax = 25; CoefficientList[Series[Exp[Exp[x] (Exp[x] - 1 - x - x^2/2 - x^3/6)], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] (2^k - 1 - k (k^2 + 5)/6) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 25}]

Crossrefs

Cf. A002663, A055882, A057837, A143405, A347432, A347434.

Sequence in context: A001925 A002663 A099855 * A003469 A364415 A189418

Adjacent sequences: A347432 A347433 A347434 * A347436 A347437 A347438

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 02 2021

Status

approved