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A347340 E.g.f.: exp( exp(exp(x) - 1) - exp(x) ). 1
1, 0, 1, 4, 17, 91, 587, 4327, 35604, 323316, 3210600, 34574453, 400893066, 4975247460, 65755573847, 921535225267, 13643496840808, 212688569520955, 3480978391442106, 59657975022473437, 1068151956803180295, 19937983367649562025, 387243759600707804811, 7812456801157894913964 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Exponential transform of A058692.

Stirling transform of A000296.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..480

FORMULA

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

a(n) = Sum_{k=0..n} Stirling2(n,k) * A000296(k).

a(n) = Sum_{k=0..n} binomial(n,k) * A000258(k) * A000587(n-k).

MAPLE

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

add(g(n-j)*binomial(n-1, j-1), j=2..n))

end:

b:= proc(n, m) option remember; `if`(n=0,

g(m), m*b(n-1, m)+b(n-1, m+1))

end:

a:= n-> b(n, 0):

seq(a(n), n=0..23); # Alois P. Heinz, Aug 27 2021

# second Maple program:

b:= proc(n, t) option remember; `if`(n=0, 1, add(b(n-j, t)*

`if`(t=0, 1, b(j, 0)-1)*binomial(n-1, j-1), j=1..n))

end:

a:= n-> b(n, 1):

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

MATHEMATICA

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

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

PROG

(PARI) my(x='x+O('x^25)); Vec(serlaplace(exp(exp(exp(x)-1)-exp(x)))) \\ Michel Marcus, Aug 27 2021

CROSSREFS

Cf. A000110, A000166, A000258, A000296, A000587, A052852, A058692, A182386, A288268.

Sequence in context: A143405 A303793 A141154 * A355295 A316084 A112354

Adjacent sequences: A347337 A347338 A347339 * A347341 A347342 A347343

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 27 2021

STATUS

approved

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Last modified December 8 12:39 EST 2022. Contains 358693 sequences. (Running on oeis4.)