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A336260
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a(0) = 1; a(n) = (n!)^4 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^4.
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6
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1, 1, 17, 1474, 404768, 271581776, 377987513392, 974814164752800, 4289222350867156992, 30232332223815625555968, 324796212685273837095714816, 5108947647642107040382284423168, 113818571142935411070742114448769024, 3492592855002964381945529723625305210880
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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(n) = (n!)^4 * [x^n] 1 / (1 - polylog(4,x)).
a(n) ~ (n!)^4 / (polylog(3,r) * r^n), where r = 0.93073451517099234709643607941... is the root of the equation polylog(4,r) = 1. - Vaclav Kotesovec, Jul 15 2020
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1,
add(b(n-i)/i^4, i=1..n))
end:
a:= n-> n!^4*b(n):
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MATHEMATICA
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a[0] = 1; a[n_] := a[n] = (n!)^4 Sum[a[k]/(k! (n - k))^4, {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]
nmax = 13; CoefficientList[Series[1/(1 - PolyLog[4, x]), {x, 0, nmax}], x] Range[0, nmax]!^4
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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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