A337677 a(0) = 1; a(n) = -(n!)^4 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^4.

1, -1, 15, -1150, 277760, -164021776, 200693093392, -455136213439776, 1760342776470958080, -10907982472777142353920, 103006437933467240856354816, -1424284967682216438413265543168, 27890228890526992620507064048877568, -752281114397558490715695708227012591616

Offset: 0

Author

Ilya Gutkovskiy, Sep 15 2020

Keywords

• sign

Crossrefs

Cf. A006252, A074706, A212857, A336260, A337676, A337678.

Programs

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

PARI

a(n)={n!^4*polcoef(1/(1 + polylog(4,x + O(x*x^n))), n)} \\ Andrew Howroyd, Sep 15 2020

Formula

Sum_{n>=0} a(n) * x^n / (n!)^4 = 1 / (1 + polylog(4,x)).