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%I #9 Sep 15 2020 21:28:34
%S 1,-1,15,-1150,277760,-164021776,200693093392,-455136213439776,
%T 1760342776470958080,-10907982472777142353920,
%U 103006437933467240856354816,-1424284967682216438413265543168,27890228890526992620507064048877568,-752281114397558490715695708227012591616
%N a(0) = 1; a(n) = -(n!)^4 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^4.
%F Sum_{n>=0} a(n) * x^n / (n!)^4 = 1 / (1 + polylog(4,x)).
%t 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}]
%t nmax = 13; CoefficientList[Series[1/(1 + PolyLog[4, x]), {x, 0, nmax}], x] Range[0, nmax]!^4
%o (PARI) a(n)={n!^4*polcoef(1/(1 + polylog(4,x + O(x*x^n))), n)} \\ _Andrew Howroyd_, Sep 15 2020
%Y Cf. A006252, A074706, A212857, A336260, A337676, A337678.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Sep 15 2020
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