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A052778
E.g.f.: x^4*log(-1/(-1+x)).
4
0, 0, 0, 0, 0, 120, 360, 1680, 10080, 72576, 604800, 5702400, 59875200, 691891200, 8717829120, 118879488000, 1743565824000, 27360571392000, 457312407552000, 8109673360588800, 152056375511040000, 3005349539512320000, 62444484876533760000, 1360632459941314560000
OFFSET
0,6
COMMENTS
Previous name was: A simple grammar.
LINKS
FORMULA
E.g.f.: x^4*log(-1/(-1+x)).
Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=120, (-n^2+3*n+4)*a(n) + (n-3)*a(n+1)}.
a(n) = n! / (n-4) (n > 4). - Olivier Gérard, Jun 13 2001
Sum_{n>=5} 1/a(n) = 49/6 - 3*e. - Amiram Eldar, Oct 07 2020
Sum_{n>=5} (-1)^(n+1)/a(n) = 5/e - 11/6. - Amiram Eldar, Aug 20 2022
MAPLE
spec := [S, {B=Cycle(Z), S=Prod(Z, Z, Z, Z, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
a[n_] := If[n < 5, 0, n!/(n - 4)]; Array[a, 20, 0] (* Amiram Eldar, Oct 07 2020 *)
With[{nn=30}, CoefficientList[Series[x^4 Log[-1/(x-1)], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jun 28 2021 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
New name using e.g.f. from Vaclav Kotesovec, Oct 07 2020
STATUS
approved