A052751 A simple grammar.

1, 1, 4, 19, 107, 647, 4167, 27847, 191747, 1349743, 9671316, 70297105, 517079157, 3841701488, 28787546360, 217317367487, 1651144126659, 12616570941114, 96891439504019, 747452640586114, 5789461514134881

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 707

Crossrefs

Cf. A006964.

Programs

Maple

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

PARI

{a(n)=local(A=1+x+x*O(x^n));if(n==0,1,for(i=1,n, A=exp(sum(k=1,n,subst(x*A^3,x,x^k+x*O(x^n))/k)));polcoeff(A,n,x))} \\ Paul D. Hanna, Jul 13 2006

Formula

G.f.: A(x) = exp(A(x)^3*x + A(x^2)^3*x^2/2 + A(x^3)^3*x^3/3 +...), A(0)=1; also, A(x)^3 = Sum_{n>=0} A006964(n+1)*x^n. - Paul D. Hanna, Jul 13 2006