A052836 - OEIS

%I #22 Jan 13 2025 10:23:53

%S 0,1,2,5,16,54,197,746,2916,11650,47418,195794,818347,3455173,

%T 14715502,63143438,272721871,1184697735,5172610484,22687623448,

%U 99918182347,441676607009,1958937661272,8714945481375,38879831980104,173900631360760,779664865945693

%N INVERT transform of A052879.

%C Old name was: A simple grammar.

%H Andrew Howroyd, <a href="/A052836/b052836.txt">Table of n, a(n) for n = 0..200</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=803">Encyclopedia of Combinatorial Structures 803</a>

%F G.f.: 1/(1 - x*g(x)) - 1 where g(x) is the g.f. of A052879. - _Andrew Howroyd_, Aug 09 2020

%F a(n) ~ c * d^n / n^(3/2), where d = 4.75339125839792507... and c = 0.26062697411657... - _Vaclav Kotesovec_, Jul 08 2021

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

%o (PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v,n,(-1)^(n-1)/n))))-1,-#v)}

%o 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

%Y Cf. A052879.

%K easy,nonn,changed

%O 0,3

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