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A336999
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a(n) = n! * Sum_{d|n} n^d / d!.
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0
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1, 8, 45, 544, 3725, 89856, 858823, 25271296, 434776329, 13241728000, 285750755411, 11494661861376, 302956057862653, 12945137688641536, 446924199188379375, 20735627677666902016, 827246308572614396177, 43155924331583693389824
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = n! * [x^n] Sum_{k>=1} (exp(n*x^k) - 1).
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MATHEMATICA
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Table[n! Sum[n^d/d!, {d, Divisors[n]}], {n, 1, 18}]
Table[n! SeriesCoefficient[Sum[(Exp[n x^k] - 1), {k, 1, n}], {x, 0, n}], {n, 1, 18}]
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PROG
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(PARI) a(n) = n! * sumdiv(n, d, n^d/d!); \\ Michel Marcus, Aug 12 2020
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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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