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A291507
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a(n) = (n!)^9 * Sum_{i=1..n} 1/i^9.
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5
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0, 1, 513, 10097891, 2647111616000, 5170142516807540224, 52103129720841632885243904, 2102549272223560776918400601161728, 282199388424234851655058321255905292713984, 109329825340451764123791003609208862665771818418176
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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^9+(n+1)^9)*a(n) - n^18*a(n-1) for n > 0.
a(n) ~ zeta(9) * (2*Pi)^(9/2) * n^(9*n+9/2) / exp(9*n). - Vaclav Kotesovec, Aug 27 2017
Sum_{n>=0} a(n) * x^n / (n!)^9 = polylog(9,x) / (1 - x). - Ilya Gutkovskiy, Jul 15 2020
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MATHEMATICA
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Table[(n!)^9 * Sum[1/i^9, {i, 1, n}], {n, 0, 12}] (* Vaclav Kotesovec, Aug 27 2017 *)
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PROG
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(PARI) a(n) = n!^9*sum(i=1, n, 1/i^9); \\ 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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