A052829 A simple grammar: partial sums of A052870.

0, 1, 2, 4, 10, 25, 69, 197, 583, 1762, 5441, 17042, 54072, 173334, 560659, 1827306, 5995570, 19787135, 65643226, 218777532, 732181107, 2459576149, 8290442750, 28031056619, 95045477945, 323112137130, 1101073839413, 3760472582922, 12869488098939, 44127605854574

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 794

Crossrefs

Cf. A052870 (first differences).

Programs

Maple

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

Formula

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

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

Extensions

More terms from Alois P. Heinz, Mar 16 2016