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A355376
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a(n) = Sum_{k=0..n} k! * (-k)^(n-k) * Stirling2(n,k).
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1
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1, 1, 1, -5, -29, 271, 3091, -61025, -744029, 34875871, 211095331, -37415273345, 300267009571, 61080483836191, -2133136977892829, -119576844586022465, 11752559492568148771, 94348367247493654111, -68793303669649907424989, 2764486881197709482575615
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OFFSET
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0,4
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LINKS
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FORMULA
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E.g.f.: Sum_{k>=0} (1 - exp(-k * x))^k / k^k.
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MATHEMATICA
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a[n_] := Sum[k! * (-k)^(n - k) * StirlingS2[n, k], {k, 0, n}]; a[0] = 1; Array[a, 20, 0] (* Amiram Eldar, Jun 30 2022 *)
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PROG
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(PARI) a(n) = sum(k=0, n, k!*(-k)^(n-k)*stirling(n, k, 2));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (1-exp(-k*x))^k/k^k)))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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