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A368719
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a(n) = n! * Sum_{k=0..n} k^5 / k!.
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2
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0, 1, 34, 345, 2404, 15145, 98646, 707329, 5691400, 51281649, 512916490, 5642242441, 67707158124, 880193426905, 12322708514494, 184840628476785, 2957450056677136, 50276650964931169, 904979717370650610, 17194614630044837689, 343892292600899953780
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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^5.
E.g.f.: B_5(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, 5, stirling(5, k, 2)*x^k)*exp(x)/(1-x))))
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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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