A253184 Triangle T(n,m) = Sum_{k=1..(n-m)/2} C(m, k)*T((n-m)/2, k), T(n,n)=1.

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, 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, 0, 0, 0, 13, 0, 26, 0, 28, 0, 10, 0, 1

Offset: 1

Author

Vladimir Kruchinin, Mar 23 2015

Keywords

• nonn
• tabl

Examples

			First few rows are:
1;
0, 1;
1, 0, 1;
0, 2, 0, 1;
0, 0, 3, 0, 1;
0, 1, 0, 4, 0, 1;
		

Crossrefs

Cf. A036987.

Programs

Maxima

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

Formula

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

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