A133601 A007318 * (A097806 + A133080 - I), I = Identity matrix.

1, 3, 1, 5, 3, 1, 7, 6, 5, 1, 9, 10, 14, 5, 1, 11, 15, 30, 15, 7, 1, 13, 21, 55, 35, 27, 7, 1, 15, 28, 91, 70, 77, 28, 9, 1, 17, 36, 140, 126, 182, 84, 44, 9, 1, 19, 45, 204, 210, 378, 210, 156, 45, 11, 1

Offset: 0

Author

Gary W. Adamson, Sep 18 2007

Keywords

• nonn
• tabl

Examples

			First few rows of the triangle are:
1;
3, 1;
5, 3, 1;
7, 6, 5, 1;
9, 10, 14, 5, 1;
11, 15, 30, 15, 7, 1;
13, 21, 55, 35, 27, 7, 1;
15, 28, 91, 70, 77, 28, 9, 1;
...
		

Crossrefs

Cf. A097806, A133080, A052549 (row sums).

Programs

Maple

A133601aux := proc(n,k)
    if n <> k then
        A097806(n,k)+A133080(n,k) ;
    else
        A097806(n,k)+A133080(n,k)-1 ;
    end if;
end proc:
A133601 := proc(n,k)
    add( A007318(n,j)*A133601aux(j+1,k+1),j=k..n) ;
end proc: # R. J. Mathar, Jun 20 2015

Formula

A007318 * (A097806 + A133080 - I), I = Identity matrix. Binomial transform of an infinite lower triangular matrix with (1,1,1,...) in the main diagonal and (2,1,2,1,2,...) in the subdiagonal; and the rest zeros.