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A347434
E.g.f.: exp( exp(x) * (exp(x) - 1 - x - x^2 / 2) ).
2
1, 0, 0, 1, 5, 16, 52, 274, 1990, 14354, 99704, 730225, 6061013, 56151330, 551040830, 5597109717, 59324775741, 664973687438, 7891158217876, 98253448977890, 1273082291906394, 17124091446383666, 239333235895599762, 3476600533730954761, 52394273274018321421
OFFSET
0,5
COMMENTS
Exponential transform of A002662.
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002662(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*(j+1)/2-1), j=1..n))
end:
seq(a(n), n=0..24); # Alois P. Heinz, Sep 02 2021
MATHEMATICA
nmax = 24; CoefficientList[Series[Exp[Exp[x] (Exp[x] - 1 - x - x^2/2)], {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 + 1)/2) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 02 2021
STATUS
approved