A052619 Expansion of e.g.f. 3*x^3/(1-x).

0, 0, 0, 18, 72, 360, 2160, 15120, 120960, 1088640, 10886400, 119750400, 1437004800, 18681062400, 261534873600, 3923023104000, 62768369664000, 1067062284288000, 19207121117184000, 364935301226496000, 7298706024529920000, 153272826515128320000, 3372002183332823040000

Offset

0,4

Links

Table of n, a(n) for n=0..22.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 564

Formula

E.g.f.: -3*x^3/(-1+x).

Recurrence: {a(0)=0, a(1)=0, a(2)=0, a(3)=18, (-1-n)*a(n)+a(n+1)=0}

a(n) = 3*n!, n>2.

E.g.f.: G(0)*3*x^3 where G(k) = 1 + x/(1 - x/(x + 1/G(k+1))); (continued fraction, 3rd kind, 3-step). - Sergei N. Gladkovskii, Jul 28 2012

Maple

spec := [S, {S=Prod(Z, Z, Sequence(Z), Union(Z, Z, Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

With[{nn=30}, CoefficientList[Series[3 x^3/(1-x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 15 2025 *)

Crossrefs

Sequence in context: A069058 A262000 A007276 * A110753 A154670 A394757

Adjacent sequences: A052616 A052617 A052618 * A052620 A052621 A052622

Keyword

easy,nonn

Author

INRIA Encyclopedia of Combinatorial Structures, Jan 25 2000

Extensions

More terms from Michel Marcus, Oct 22 2025

Status

approved