A337676 a(0) = 1; a(n) = -(n!)^3 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^3.

1, -1, 7, -170, 9664, -1080824, 207876968, -63709383408, 29068641741312, -18924533538121728, 16870738405288439808, -20048074289311310521344, 30889296893650981899202560, -60580966918820974514054369280, 148238116513927185591120536580096

Offset: 0

Author

Ilya Gutkovskiy, Sep 15 2020

Keywords

• sign

Crossrefs

Cf. A006252, A074706, A212856, A336259, A337677, A337678.

Programs

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

PARI

a(n)={n!^3*polcoef(1/(1 + polylog(3,x + O(x*x^n))), n)} \\ Andrew Howroyd, Sep 15 2020

Formula

Sum_{n>=0} a(n) * x^n / (n!)^3 = 1 / (1 + polylog(3,x)).