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A343928
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a(n) = Sum_{k=0..n} (k!)^n * binomial(n,k).
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3
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1, 2, 7, 244, 337061, 24923091206, 139331988275478727, 82607113404338664216300296, 6984967577834038055008791270166057993, 109110690950275218023122492287310115968068596613130, 395940866518366059877297056617763923418318903997411043997258716171
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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) = [x^n] Sum_{k>=0} (k!)^n * x^k/(1 - x)^(k+1).
a(n) = n! * [x^n] exp(x) * Sum_{k>=0} (k!)^(n-1) * x^k.
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MATHEMATICA
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a[n_] := Sum[(k!)^n * Binomial[n, k], {k, 0, n} ]; Array[a, 11, 0] (* Amiram Eldar, May 04 2021 *)
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PROG
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(PARI) a(n) = sum(k=0, n, k!^n*binomial(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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