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A346056
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Expansion of e.g.f. Product_{k>=1} B(x^k/k!) where B(x) = exp(exp(x) - 1) = e.g.f. of Bell numbers.
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4
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1, 1, 3, 9, 38, 168, 915, 5225, 34228, 236622, 1805297, 14498751, 125907798, 1146476984, 11129874215, 112934907867, 1209762361679, 13499714095281, 157931096158594, 1918777335806274, 24309294470496502, 318987321135326838, 4346474397776153974
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: exp( Sum_{k>=1} (exp(x^k/k!) - 1) ).
E.g.f.: exp( Sum_{k>=1} A038041(k)*x^k/k! ).
a(n) = (n-1)! * Sum_{k=1..n} k * (Sum_{d|k} 1/(d! * (k/d)!^d)) * a(n-k)/(n-k)! for n > 0.
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PROG
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(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, exp(exp(x^k/k!)-1))))
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, exp(x^k/k!)-1))))
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, sumdiv(k, d, 1/(d!*(k/d)!^d))*x^k))))
(PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=1, n, k*sumdiv(k, d, 1/(d!*(k/d)!^d))*a(n-k)/(n-k)!));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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