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%I #14 Jun 13 2017 22:09:51
%S 1,1,1,1,2,1,1,3,5,1,1,4,10,10,1,1,5,18,28,17,1,1,6,27,74,69,26,1,1,7,
%T 39,137,245,151,37,1,1,8,52,236,586,676,298,50,1,1,9,68,372,1194,2126,
%U 1634,540,65,1,1,10,85,552,2322,5152,6620,3578,913,82,1,1,11,105,777,3954,12002,19292,18082,7249,1459,101,1
%N Triangle, read by rows, where the n-th diagonal equals the n-th row transformed by triangle A008459 (squared binomial coefficients).
%C Row sums form A097085.
%H Alois P. Heinz, <a href="/A097084/b097084.txt">Rows n = 0..140, flattened</a>
%F T(n,k) = Sum_{j=0..k} T(n-k,j)*C(k,j)^2.
%e T(8,3) = 236 = (1)*1^2 + (5)*3^2 + (18)*3^2 + (28)*1^2
%e = Sum_{j=0..3} T(5,j)*C(3,j)^2.
%e Rows begin:
%e [1],
%e [1,1],
%e [1,2,1],
%e [1,3,5,1],
%e [1,4,10,10,1],
%e [1,5,18,28,17,1],
%e [1,6,27,74,69,26,1],
%e [1,7,39,137,245,151,37,1],
%e [1,8,52,236,586,676,298,50,1],...
%p T:= proc(n, k) option remember;
%p `if`(n=k or k=0, 1, `if`(k<0 or k>n, 0,
%p add(T(n-k, j)*binomial(k, j)^2, j=0..k)))
%p end:
%p seq(seq(T(n,k), k=0..n), n=0..12); # _Alois P. Heinz_, Oct 30 2015
%t T[_, 0] = 1; T[n_, n_] = 1; T[n_, k_] /; 0 < k < n := T[n, k] = Sum[T[n - k, j]*Binomial[k, j]^2, {j, 0, k}]; T[_, _] = 0;
%t Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, May 24 2016 *)
%o (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)*binomial(k,j)^2)))
%Y Cf. A097085, A008459.
%K nonn,tabl
%O 0,5
%A _Paul D. Hanna_, Jul 23 2004
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