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

0,3

Links

Table of n, a(n) for n=0..20.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 707

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

Maple

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

Prog

(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

Crossrefs

Cf. A006964.

Sequence in context: A082030 A348802 A379513 * A367284 A249934 A174992

Adjacent sequences: A052748 A052749 A052750 * A052752 A052753 A052754

Keyword

easy,nonn

Author

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

Status

approved