A052587 Expansion of e.g.f. x^2*(1-x)/(1-2*x).

0, 0, 2, 6, 48, 480, 5760, 80640, 1290240, 23224320, 464486400, 10218700800, 245248819200, 6376469299200, 178541140377600, 5356234211328000, 171399494762496000, 5827582821924864000, 209792981589295104000

Offset

0,3

Comments

Essentially the same as A051578. - R. J. Mathar, Feb 22 2008

Links

Table of n, a(n) for n=0..18.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 532

Formula

E.g.f.: x^2*(-1+x)/(-1+2*x).

Recurrence: a(0) = a(1) = 0, a(2) = 2, a(3) = 6, a(n+1) = 2*(n+1)*a(n) for n > 3.

a(n) = 1/8*2^n*n!, n > 2.

a(n) = A051578(n-2) = (2*n)!!/4!! for n > 2. - M. F. Hasler, Nov 10 2024

Maple

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

Prog

(PARI) apply( {A052587(n)=n!<<(n-3)+(n==2)}, [0..19]) \\ M. F. Hasler, Nov 10 2024

Crossrefs

Cf. A051578 (essentially the same), A000165 (double factorial), A000142 (factorial), A000079 (powers of 2).

Sequence in context: A195203 A365285 A052743 * A052735 A365286 A052717

Adjacent sequences: A052584 A052585 A052586 * A052588 A052589 A052590

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Status

approved