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A291506
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a(n) = (n!)^8 * Sum_{i=1..n} 1/i^8.
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5
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0, 1, 257, 1686433, 110523752704, 43173450975314176, 72514862031522895036416, 418033821374598847702425993216, 7013444132843374500928464765799366656, 301905779820559925981495987360836056017534976
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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(1) = 1, a(n+1) = (n^8+(n+1)^8)*a(n) - n^16*a(n-1) for n > 0.
a(n) ~ 8 * Pi^12 * n^(8*n+4) / (4725 * exp(8*n)). - Vaclav Kotesovec, Aug 27 2017
Sum_{n>=0} a(n) * x^n / (n!)^8 = polylog(8,x) / (1 - x). - Ilya Gutkovskiy, Jul 15 2020
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MATHEMATICA
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Table[(n!)^8 * Sum[1/i^8, {i, 1, n}], {n, 0, 15}] (* Vaclav Kotesovec, Aug 27 2017 *)
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PROG
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(PARI) a(n) = n!^8*sum(i=1, n, 1/i^8); \\ Michel Marcus, Aug 26 2017
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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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