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A336260 a(0) = 1; a(n) = (n!)^4 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^4. 4
1, 1, 17, 1474, 404768, 271581776, 377987513392, 974814164752800, 4289222350867156992, 30232332223815625555968, 324796212685273837095714816, 5108947647642107040382284423168, 113818571142935411070742114448769024, 3492592855002964381945529723625305210880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..13.

FORMULA

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

MATHEMATICA

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

CROSSREFS

Cf. A007840, A217145, A336196, A336258, A336259, A336261.

Sequence in context: A242282 A129911 A336196 * A104808 A061686 A133590

Adjacent sequences:  A336257 A336258 A336259 * A336261 A336262 A336263

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 15 2020

STATUS

approved

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Last modified August 3 01:53 EDT 2021. Contains 346429 sequences. (Running on oeis4.)