A316862 Expansion of 1/(Sum_{k>=0} (k!)^3 x^k).

1, -1, -7, -201, -13351, -1697705, -369575303, -127249900617, -65286578868455, -47651775381867241, -47688241963081263175, -63505249400026210723209, -109775495351620406817045415, -241236985075124408660287423529, -662075390371447206867029299628807

Offset: 0

Author

Seiichi Manyama, Jul 15 2018

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..181

Crossrefs

1/(Sum_{k>=0} (k!)^b x^k): A167894 (b=1), A113871 (b=2), this sequence (b=3).

Cf. A000442.

Programs

Mathematica

a[n_] := -Sum[(k!)^3*a[n - k], {k, n}]; a[0] = 1; Array[a, 15, 0] (* Robert G. Wilson v, Jul 15 2018 *)
nmax = 20; CoefficientList[Series[1/Sum[k!^3 * x^k, {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 08 2020 *)

Formula

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

a(n) ~ -(n!)^3 * (1 - 2/n^3 - 13/n^6 - 39/n^7 - 78/n^8 - 518/n^9 - 3687/n^10 - ...). - Vaclav Kotesovec, Dec 08 2020