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A307066
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a(n) = exp(-1) * Sum_{k>=0} (n*k + 1)^n/k!.
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5
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1, 2, 13, 199, 5329, 216151, 12211597, 909102342, 85761187393, 9957171535975, 1390946372509101, 229587693339867567, 44117901231194922193, 9748599124579281064294, 2451233017637221706477037, 695088863051920283838281851, 220558203335628758134165860609
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = n! * [x^n] exp(exp(n*x) + x - 1).
a(n) = Sum_{k=0..n} binomial(n,k) * n^k * Bell(k).
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MATHEMATICA
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Table[Exp[-1] Sum[(n k + 1)^n/k!, {k, 0, Infinity}], {n, 0, 16}]
Table[n! SeriesCoefficient[Exp[Exp[n x] + x - 1], {x, 0, n}], {n, 0, 16}]
Join[{1}, Table[Sum[Binomial[n, k] n^k BellB[k], {k, 0, n}], {n, 1, 16}]]
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PROG
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(Magma)
A307066:= func< n | (&+[Binomial(n, k)*n^k*Bell(k): k in [0..n]]) >;
(SageMath)
def A307066(n): return sum(binomial(n, k)*n^k*bell_number(k) for k in range(n+1))
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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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