A052836 INVERT transform of A052879.

0, 1, 2, 5, 16, 54, 197, 746, 2916, 11650, 47418, 195794, 818347, 3455173, 14715502, 63143438, 272721871, 1184697735, 5172610484, 22687623448, 99918182347, 441676607009, 1958937661272, 8714945481375, 38879831980104, 173900631360760, 779664865945693

Offset

0,3

Comments

Old name was: A simple grammar.

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 803

Formula

G.f.: 1/(1 - x*g(x)) - 1 where g(x) is the g.f. of A052879. - Andrew Howroyd, Aug 09 2020

a(n) ~ c * d^n / n^(3/2), where d = 4.75339125839792507... and c = 0.26062697411657... - Vaclav Kotesovec, Jul 08 2021

Maple

spec := [S, {B=Prod(Z, C), S=Sequence(B, 1 <= card), C= PowerSet(S)}, 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=[]); for(n=1, n, v=Vec(1/(1-x-x^2*Ser(WeighT(v))) - 1)); concat([0], v)} \\ Andrew Howroyd, Aug 09 2020

Crossrefs

Cf. A052879.

Sequence in context: A149966 A149967 A148400 * A108526 A363201 A321470

Adjacent sequences: A052833 A052834 A052835 * A052837 A052838 A052839

Keyword

easy,nonn,changed

Author

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

Status

approved