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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

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OFFSET

0,3

LINKS

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

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

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 *)

CROSSREFS

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

Cf. A000442.

Sequence in context: A355087 A276537 A233507 * A226414 A226345 A361141

Adjacent sequences: A316859 A316860 A316861 * A316863 A316864 A316865

KEYWORD

sign

AUTHOR

Seiichi Manyama, Jul 15 2018

STATUS

approved

URL: https://oeis.org/A316862

⇱ A316862 - OEIS