A052589 a(n) = (2^n - 1)*n!.

0, 1, 6, 42, 360, 3720, 45360, 640080, 10281600, 185431680, 3712262400, 81709689600, 1961511552000, 51005527372800, 1428241944729600, 42848566016256000, 1371175035310080000, 46620306887970816000, 1678337450340655104000, 63776944758045302784000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 534

Crossrefs

Cf. A000165.

Programs

Maple

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

Mathematica

Table[(2^n-1)n!,{n,0,20}] (* Harvey P. Dale, Jul 18 2015 *)

PARI

{a(n) = if( n<0, 0, (2^n - 1)*n!)}; /* Michael Somos, Jul 22 2017 */

Formula

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

D-finite with Recurrence: {a(1)=1, a(0)=0, (2*n^2 + 6*n + 4)*a(n) + (-6 - 3*n)*a(n+1) + a(n+2) = 0}.

G.f.: -G(0) where G(k) = 1 - 2^k/(1 - x*(k+1)/(x*(k+1) - 2^k/G(k+1) )), (continued fraction). - Sergei N. Gladkovskii, Dec 06 2012

From Michael Somos, Jul 22 2017: (Start)

If A(x) = Sum_{k>0} x^k / a(k), then A(2*x) = A(x) + e^x - 1.

0 = +a(n)*(+1104*a(n+3) -792*a(n+4) +136*a(n+5) -6*a(n+6)) +a(n+1)*(+828*a(n+3) -435*a(n+4) +39*a(n+5)) + a(n+2)*(+299*a(n+3) -102*a(n+4)) +a(n+3)*(+69*a(n+3)) for n>=0. (End)