A052870 First differences of A052829.

1, 1, 2, 6, 15, 44, 128, 386, 1179, 3679, 11601, 37030, 119262, 387325, 1266647, 4168264, 13791565, 45856091, 153134306, 513403575, 1727395042, 5830866601, 19740613869, 67014421326, 228066659185, 777961702283, 2659398743509, 9109015516017, 31258117755635

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Old name was: A simple grammar.

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 841

Crossrefs

Cf. A052829, A052855.

Programs

Maple

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

Formula

From Seiichi Manyama, Jun 07 2023: (Start)

Conjectures: G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * x^k/(k * (1 - x^k)) ).

A(x) = Sum_{k>=0} a(k) * x^k = Product_{j>=1} Product_{k>=0} (1+x^(j+k))^a(k). (End)

Extensions

More terms from Alois P. Heinz, Mar 16 2016