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A092422 Triangle, read by rows, where T(n,k) equals the k-th term of the convolution of the (n-k)-th row with the (2k)-th Fibonacci polynomial (A011973).

%I A092422 #6 Jun 13 2017 21:52:40
%S A092422 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,
%T A092422 30,72,98,66,22,1,1,8,40,119,211,214,113,29,1,1,9,52,182,398,546,428,
%U A092422 183,37,1,1,10,65,265,692,1170,1278,799,283,46,1,1,11,80,368,1123,2286,3104
%N A092422 Triangle, read by rows, where T(n,k) equals the k-th term of the convolution of the (n-k)-th row with the (2k)-th Fibonacci polynomial (A011973).
%F A092422 T(n, k) = sum_{j=0, min(k, n-k)} binomial(k+j, k-j)*T(n-k, j) with T(n, 0)=1.
%e A092422 Even-numbered Fibonacci polynomials (cf. A011973) are:
%e A092422 {1},
%e A092422 {1,1},
%e A092422 {1,3,1},
%e A092422 {1,5,6,1},
%e A092422 {1,7,15,10,1},...
%e A092422 These terms are used to generate each row from the prior rows. For example,
%e A092422 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)};
%e A092422 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)}.
%e A092422 Rows begin:
%e A092422 {1},
%e A092422 {1,1},
%e A092422 {1,2,1},
%e A092422 {1,3,4,1},
%e A092422 {1,4,8,7,1},
%e A092422 {1,5,14,18,11,1},
%e A092422 {1,6,21,40,36,16,1},
%e A092422 {1,7,30,72,98,66,22,1},
%e A092422 {1,8,40,119,211,214,113,29,1},
%e A092422 {1,9,52,182,398,546,428,183,37,1},...
%o A092422 (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))))
%Y A092422 Cf. A092423, A092424, A011973.
%K A092422 nonn,tabl
%O A092422 0,5
%A A092422 _Paul D. Hanna_, Mar 22 2004