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A339401
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a(n) = numerator of (1/e)^n * Sum_{k>=0}(n^k*k^n)/(n!*k!).
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1
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1, 1, 3, 19, 63, 322, 44683, 941977, 4677605, 668520163, 21622993111, 9759873853, 31135480907413, 194137920764803, 64440211018897379, 3298807094967155971, 181322497435007616497, 532556590750629416219, 665881649529214120845679, 2596711638295426703997397, 1031081559092352146579024047
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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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a(n) = numerator([x^n] exp(n*(exp(x)-1))). - Alois P. Heinz, Dec 07 2020
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MAPLE
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A:= proc(n, k) option remember; `if`(n=0, 1, (1+
add(binomial(n-1, j-1)*A(n-j, k), j=1..n-1))*k)
end:
a:= n-> numer(A(n$2)/n!):
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MATHEMATICA
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a[n_] := BellB[n, n]/n! // Numerator;
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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