A253190 Triangle T(n, m)=Sum_{k=1..(n-m)/2} C(m+k-1, k)*T((n-m)/2, k), T(n,n)=1.

1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 3, 0, 1, 0, 3, 0, 4, 0, 1, 2, 0, 6, 0, 5, 0, 1, 0, 6, 0, 10, 0, 6, 0, 1, 3, 0, 13, 0, 15, 0, 7, 0, 1, 0, 11, 0, 24, 0, 21, 0, 8, 0, 1, 5, 0, 27, 0, 40, 0, 28, 0, 9, 0, 1, 0, 20, 0, 55, 0, 62, 0, 36, 0, 10, 0, 1

Offset: 1

Author

Vladimir Kruchinin, Mar 24 2015

Keywords

• nonn
• tabl

Examples

			1;
0, 1;
1, 0, 1;
0, 2, 0, 1;
1, 0, 3, 0, 1;
0, 3, 0, 4, 0, 1;
2, 0, 6, 0, 5, 0, 1;
		

Crossrefs

Cf. A000621 (row sums), A003600, A253184, A253189.

Programs

Maple

A253190 := proc(n,m)
    option remember;
    if n = m then
        1;
    elif type(n-m,'odd') then
        0 ;
    else
        add(binomial(m+k-1,k)*procname((n-m)/2,k),k=1..(n-m)/2) ;
    end if;
end proc: # R. J. Mathar, Dec 16 2015

Maxima

T(n, m):=if n=m then 1 else sum(binomial(m+k-1, 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, A(x)=Sum_{n>0} a(n)*x^(2*n-1), a(n) - is A000621.