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A336259
a(0) = 1; a(n) = (n!)^3 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^3.
6
1, 1, 9, 278, 20464, 2948824, 735078968, 291153023664, 172201253334528, 145044581320046592, 167609226267379703808, 257816558769660828601344, 514890814087717253133447168, 1307445058678686737908660752384, 4146656933568759002389401276616704
OFFSET
0,3
LINKS
FORMULA
a(n) = (n!)^3 * [x^n] 1 / (1 - polylog(3,x)).
a(n) ~ (n!)^3 / (polylog(2,r) * r^n), where r = 0.86512013798076629268795131756... is the root of the equation polylog(3,r) = 1. - Vaclav Kotesovec, Jul 15 2020
MAPLE
b:= proc(n) option remember; `if`(n=0, 1,
add(b(n-i)/i^3, i=1..n))
end:
a:= n-> n!^3*b(n):
seq(a(n), n=0..14); # Alois P. Heinz, Jan 04 2024
MATHEMATICA
a[0] = 1; a[n_] := a[n] = (n!)^3 Sum[a[k]/(k! (n - k))^3, {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]
nmax = 14; CoefficientList[Series[1/(1 - PolyLog[3, x]), {x, 0, nmax}], x] Range[0, nmax]!^3
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 15 2020
STATUS
approved