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A351281
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a(n) = Sum_{k=0..n} k! * k^k * Stirling2(n,k).
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2
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1, 1, 9, 187, 7173, 440611, 39631509, 4910795107, 802015652853, 166948755155971, 43146953460348309, 13555255072473665827, 5087595330217093070133, 2248298922174973220446531, 1155512971750307157457879509, 683392198848998191062416885347
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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(x) - 1))^k.
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MATHEMATICA
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a[0] = 1; a[n_] := Sum[k! * k^k * StirlingS2[n, k], {k, 1, n}]; Array[a, 16, 0] (* Amiram Eldar, Feb 06 2022 *)
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PROG
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(PARI) a(n) = sum(k=0, n, k!*k^k*stirling(n, k, 2));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*(exp(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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