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A347339
E.g.f.: exp( (exp(x) - 1) * exp(exp(x) - 1) ).
2
1, 1, 4, 20, 123, 902, 7656, 73509, 785154, 9213324, 117624569, 1621028312, 23959376436, 377730250003, 6322478398476, 111904530008040, 2087093471665987, 40891426070289970, 839329531471890724, 18004595602417946685, 402747680140030433886, 9376084240910510840672, 226760664399026618376569
OFFSET
0,3
COMMENTS
Exponential transform of A138378.
Stirling transform of A000248.
LINKS
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * (Bell(k+1) - Bell(k)) * a(n-k).
a(n) = Sum_{k=0..n} Stirling2(n,k) * A000248(k).
MAPLE
g:= proc(n) option remember; `if`(n=0, 1,
add(g(n-j)*j*binomial(n-1, j-1), j=1..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..22); # Alois P. Heinz, Aug 27 2021
MATHEMATICA
nmax = 22; CoefficientList[Series[Exp[(Exp[x] - 1) Exp[Exp[x] - 1]], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] (BellB[k + 1] - BellB[k]) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]
PROG
(PARI) my(x='x+O('x^25)); Vec(serlaplace(exp((exp(x)-1)*exp(exp(x)-1)))) \\ Michel Marcus, Aug 27 2021
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 27 2021
STATUS
approved