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

%I A253184 #16 Mar 24 2015 19:04:47
%S A253184 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 A253184 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 A253184 0,0,0,13,0,26,0,28,0,10,0,1
%N A253184 Triangle T(n,m) = Sum_{k=1..(n-m)/2} C(m, k)*T((n-m)/2, k), T(n,n)=1.
%F A253184 G.f.: A(x)^m = Sum_{n>=m} T(n,m)*x^n, where A(x) = Sum_{n>0} x^(2^n-1).
%F A253184 (1+A(x)) is g.f. of Fredholm-Rueppel sequence (A036987).
%e A253184 First few rows are:
%e A253184 1;
%e A253184 0, 1;
%e A253184 1, 0, 1;
%e A253184 0, 2, 0, 1;
%e A253184 0, 0, 3, 0, 1;
%e A253184 0, 1, 0, 4, 0, 1;
%o A253184 (Maxima)
%o A253184 T(n, m):=if n=m then 1 else sum(binomial(m, k)*T((n-m)/2, k), k, 1, (n-m)/2);
%Y A253184 Cf. A036987.
%K A253184 nonn,tabl
%O A253184 1,8
%A A253184 _Vladimir Kruchinin_, Mar 23 2015