A113711 Triangle, read by rows, where row n forms a polynomial in y=2*k that generates diagonal n as k=0,1,2,... for n>=0; thus T(n,k) = Sum_{j=0..n-k} T(n-k,j)*(2*k)^j, with T(n,0)=T(n,n)=1.

1, 1, 1, 1, 3, 1, 1, 11, 5, 1, 1, 51, 29, 7, 1, 1, 291, 189, 55, 9, 1, 1, 1955, 1373, 463, 89, 11, 1, 1, 14947, 11037, 4159, 921, 131, 13, 1, 1, 127203, 97565, 39871, 9945, 1611, 181, 15, 1, 1, 1188067, 942109, 408703, 112217, 20411, 2581, 239, 17, 1

Offset

0,5

Links

Table of n, a(n) for n=0..54.

Example

Triangle begins:
1;
1,1;
1,3,1;
1,11,5,1;
1,51,29,7,1;
1,291,189,55,9,1;
1,1955,1373,463,89,11,1;
1,14947,11037,4159,921,131,13,1;
1,127203,97565,39871,9945,1611,181,15,1;
1,1188067,942109,408703,112217,20411,2581,239,17,1; ...
where diagonals are generated by row polynomials:
T(6,5) = (1) + (1)*(2*5) = 11.
T(6,4) = (1) + (3)*(2*4) + (1)*(2*4)^2 = 89.
T(6,3) = (1) + (11)*(2*3) + (5)*(2*3)^2 + (1)*(2*3)^3 = 463.
T(6,2) = (1) + (51)*(2*2) + (29)*(2*2)^2 + (7)*(2*2)^3 + (1)*(2*2)^4 = 1373.

Prog

(PARI) T(n, k)=if(n<k || k<0, 0, if(n==k || k==0, 1, sum(j=0, n-k, T(n-k, j)*(2*k)^j)))

Crossrefs

Cf. A091150, A113716, A113712 (column 1), A113713 (column 2), A113714 (column 3), A113715 (row sums).

Sequence in context: A082466 A120270 A243752 * A339019 A257894 A103997

Adjacent sequences: A113708 A113709 A113710 * A113712 A113713 A113714

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 08 2005

Status

approved