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A350722
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a(n) = Sum_{k=0..n} k! * k^(k+n) * Stirling2(n,k).
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4
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1, 1, 33, 4567, 1652493, 1235777551, 1656820330173, 3619858882041487, 12034209740498292093, 57813156798714532953391, 385490564193781368103929213, 3454086424032897924417605526607, 40500898779980258599522326286912893
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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.: Sum_{k>=0} (k * (exp(k*x) - 1))^k.
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MATHEMATICA
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a[0] = 1; a[n_] := Sum[k! * k^(k+n) * StirlingS2[n, k], {k, 1, n}]; Array[a, 13, 0] (* Amiram Eldar, Feb 03 2022 *)
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PROG
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(PARI) a(n) = sum(k=0, n, k!*k^(k+n)*stirling(n, k, 2));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*(exp(k*x)-1))^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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