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A368716
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a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * k^3 / k!.
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1
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0, 1, 6, 9, 28, -15, 306, -1799, 14904, -133407, 1335070, -14684439, 176214996, -2290792751, 32071101258, -481066515495, 7697064252016, -130850092279359, 2355301661034294, -44750731559644727, 895014631192902540, -18795307255050944079
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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(0) = 0; a(n) = -n*a(n-1) + n^3.
E.g.f.: B_3(x) * exp(x) / (1+x), where B_n(x) = Bell polynomials.
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PROG
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(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=0, 3, stirling(3, k, 2)*x^k)*exp(x)/(1+x))))
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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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