A052879 Number of objects generated by the Combstruct grammar defined in the Maple program. See the link for the grammer specification.

1, 1, 2, 7, 22, 81, 303, 1178, 4675, 18951, 77925, 324642, 1366718, 5806575, 24861979, 107178994, 464805955, 2026418389, 8876266930, 39045009419, 172406753611, 763909798818, 3395430555790, 15135466679592, 67646059160525, 303071133963399, 1360886676130531

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 850

Maplesoft, Combstruct grammars.

Formula

G.f.: g(x)/(x*(1 + g(x))) where g(x) is the g.f. of A052836. - Andrew Howroyd, Aug 09 2020

a(n) ~ c * d^n / n^(3/2), where d = 4.75339125839792507... and c = 0.47320316916893... - Vaclav Kotesovec, Jul 08 2021

Maple

spec := [S, {B=Sequence(C, 1 <= card), C=Prod(Z, S), S= PowerSet(B)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);

Prog

(PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}
seq(n)={my(v=[1]); for(n=1, n, v=concat([1], WeighT(Vec(1/(1-x*Ser(v))-1)))); v} \\ Andrew Howroyd, Aug 09 2020

Crossrefs

Cf. A052836.

Sequence in context: A110137 A097967 A360861 * A007867 A241156 A014558

Adjacent sequences: A052876 A052877 A052878 * A052880 A052881 A052882

Keyword

easy,nonn

Author

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

Extensions

Terms a(21) and beyond from Andrew Howroyd, Aug 09 2020

Status

approved