A052778 E.g.f.: x^4*log(-1/(-1+x)).

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

Amiram Eldar, Table of n, a(n) for n = 0..450

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 735.

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

Cf. A052747, A052794, A052759.

Sequence in context: A234915 A061218 A321841 * A354625 A354624 A226884

Adjacent sequences: A052775 A052776 A052777 * A052779 A052780 A052781

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