OFFSET
0,5
FORMULA
T(n, k) = sum_{j=0, min(k, n-k)} binomial(k+j, k-j)*T(n-k, j) with T(n, 0)=1.
EXAMPLE
Even-numbered Fibonacci polynomials (cf. A011973) are:
{1},
{1,1},
{1,3,1},
{1,5,6,1},
{1,7,15,10,1},...
These terms are used to generate each row from the prior rows. For example,
row 5 = {1(1), 1(1)+1(4), 1(1)+3(3)+1(4), 1(1)+6(2)+5(1), 1(1)+10(1), 1(1)};
row 6 = {1(1), 1(1)+1(5), 1(1)+3(4)+1(8), 1(1)+6(3)+5(4)+1(1), 1(1)+10(2)+15(1), 1(1)+15(1), 1(1)}.
Rows begin:
{1},
{1,1},
{1,2,1},
{1,3,4,1},
{1,4,8,7,1},
{1,5,14,18,11,1},
{1,6,21,40,36,16,1},
{1,7,30,72,98,66,22,1},
{1,8,40,119,211,214,113,29,1},
{1,9,52,182,398,546,428,183,37,1},...
PROG
(PARI) T(n, k)=if(n<k || k<0, 0, if(k==0, 1, sum(j=0, min(k, n-k), binomial(k+j, k-j)*T(n-k, j))))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Mar 22 2004
STATUS
approved