A052829 - OEIS

%I #22 Jun 28 2021 15:59:46

%S 0,1,2,4,10,25,69,197,583,1762,5441,17042,54072,173334,560659,1827306,

%T 5995570,19787135,65643226,218777532,732181107,2459576149,8290442750,

%U 28031056619,95045477945,323112137130,1101073839413,3760472582922,12869488098939,44127605854574

%N A simple grammar.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=794">Encyclopedia of Combinatorial Structures 794</a>

%F G.f.: (x/(1-x))*Product_{k>=1} (1+x^k)^a(k). - _Vladeta Jovovic_, Jul 22 2004

%F G.f. A(x) satisfies: A(x) = (x/(1 - x)) * exp(Sum_{k>=1} (-1)^(k+1) * A(x^k) / k). - _Ilya Gutkovskiy_, Jun 28 2021

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

%Y Cf. A052870 (first differences).

%K easy,nonn

%O 0,3

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

%E More terms from _Alois P. Heinz_, Mar 16 2016