A152560 - OEIS

%I #3 Mar 30 2012 18:37:15

%S 1,1,3,7,37,225,2707,47991,1566965,85002865,8346008131,1441358958439,

%T 452666387604933,257384373709193473,268828878795481175283,

%U 516988085848458847554135,1844678455777198460320221077

%N a(n) = A131205(A005578(n)).

%C Related to binary partitions (A000123); A131205 is defined by a(n) = a(n-1) + a(floor(n/2)) + a(ceiling(n/2)) and A005578(n) = (2^(n+1)+3+(-1)^n)/6.

%o (PARI) {a(n)=local(N=(2^(n+1)+3+(-1)^n)/6,X=x+O(x^N));polcoeff(1/((1-X)^2*prod(m=0,n-1,1-X^(2^m))),N-1)}

%Y Cf. A131205, A005578, A000123.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 22 2008