A052884 - OEIS

%I #18 Aug 10 2020 01:59:58

%S 0,1,2,6,20,73,278,1106,4519,18908,80530,348144,1523492,6736163,

%T 30046395,135041458,610954709,2780185203,12716659506,58434130086,

%U 269618874220,1248677115180,5802514845319,27046974876433,126428233339972,592506121687352,2783409839422829

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

%H Andrew Howroyd, <a href="/A052884/b052884.txt">Table of n, a(n) for n = 0..200</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=857">Encyclopedia of Combinatorial Structures 857</a>

%H Maplesoft, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=examples%2fcombstruct_grammars">Combstruct grammars</a>.

%F G.f.: 1/(1 - x*g(x)) - 1 where g(x) is the g.f. of A052872. - _Andrew Howroyd_, Aug 09 2020

%p spec := [S, {B = Prod(Z,C), S=Sequence(B, 1 <= card), C=Set(S)}, unlabeled]:

%p seq(combstruct[count](spec, size=n), n=0..20);

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

%o seq(n)={my(v=[]); for(n=1, n, v=Vec(1/(1-x-x^2*Ser(EulerT(v))) - 1)); concat([0], v)} \\ _Andrew Howroyd_, Aug 09 2020

%Y Cf. A052872.

%K easy,nonn

%O 0,3

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

%E Terms a(21) and beyond from _Andrew Howroyd_, Aug 09 2020