

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..nk} T(nk,j)*(2*k)^j, with T(n,0)=T(n,n)=1.


6



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
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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<kk<0, 0, if(n==kk==0, 1, sum(j=0, nk, T(nk, j)*(2*k)^j)))


CROSSREFS

Cf. A091150, A113716, A113712 (column 1), A113713 (column 2), A113714 (column 3), A113715 (row sums).
Sequence in context: A078688 A082466 A120270 * A103997 A223256 A013561
Adjacent sequences: A113708 A113709 A113710 * A113712 A113713 A113714


KEYWORD

nonn,tabl


AUTHOR

Paul D. Hanna, Nov 08 2005


STATUS

approved



