A253184 - OEIS

%I #16 Mar 24 2015 19:04:47

%S 1,0,1,1,0,1,0,2,0,1,0,0,3,0,1,0,1,0,4,0,1,1,0,3,0,5,0,1,0,2,0,6,0,6,

%T 0,1,0,0,4,0,10,0,7,0,1,0,2,0,8,0,15,0,8,0,1,0,0,6,0,15,0,21,0,9,0,1,

%U 0,0,0,13,0,26,0,28,0,10,0,1

%N Triangle T(n,m) = Sum_{k=1..(n-m)/2} C(m, k)*T((n-m)/2, k), T(n,n)=1.

%F G.f.: A(x)^m = Sum_{n>=m} T(n,m)*x^n, where A(x) = Sum_{n>0} x^(2^n-1).

%F (1+A(x)) is g.f. of Fredholm-Rueppel sequence (A036987).

%e First few rows are:

%e 1;

%e 0, 1;

%e 1, 0, 1;

%e 0, 2, 0, 1;

%e 0, 0, 3, 0, 1;

%e 0, 1, 0, 4, 0, 1;

%o (Maxima)

%o T(n, m):=if n=m then 1 else sum(binomial(m, k)*T((n-m)/2, k), k, 1, (n-m)/2);

%Y Cf. A036987.

%K nonn,tabl

%O 1,8

%A _Vladimir Kruchinin_, Mar 23 2015