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A347432 E.g.f.: exp( exp(x) * (exp(x) - 1 - x) ). 2
1, 0, 1, 4, 14, 66, 397, 2626, 18797, 148238, 1281134, 11943790, 118998365, 1262189748, 14203022537, 168835162632, 2111832477426, 27708387132906, 380355066174121, 5449577398256414, 81316095965242989, 1261149374033472626, 20293627142875917978, 338263983223664609198 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Exponential transform of A000295.

LINKS

Table of n, a(n) for n=0..23.

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A000295(k) * a(n-k).

a(n) = Sum_{k=0..n} (-1)^k * binomial(n,k) * A003725(k) * A143405(n-k).

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(

      a(n-j)*binomial(n-1, j-1)*(2^j-j-1), j=1..n))

    end:

seq(a(n), n=0..23);  # Alois P. Heinz, Sep 02 2021

MATHEMATICA

nmax = 23; CoefficientList[Series[Exp[Exp[x] (Exp[x] - 1 - x)], {x, 0, nmax}], x] Range[0, nmax]!

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] (2^k - k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 23}]

CROSSREFS

Cf. A000295, A000296, A003725, A055882, A143405, A347434, A347435.

Sequence in context: A320488 A126787 A187742 * A129219 A292719 A292720

Adjacent sequences:  A347429 A347430 A347431 * A347433 A347434 A347435

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 02 2021

STATUS

approved

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Last modified January 21 22:08 EST 2022. Contains 350480 sequences. (Running on oeis4.)