%I
%S 1,14,117,813,4871,27743,151208,804065,4185683,21472005,108766010,
%T 545507633,2712801330,13394412999,65722444172,320721839860,
%U 1557502222385,7530671086667,36267851679585,174038009185816,832392015517829,3969017685816667,18871416851149078
%N Column 2 of triangle A128567.
%C A128567 is the matrix square of Parker's partition triangle A047812.
%F a(n) = Sum_{s=2..n+2} A047812(n+3,s)*A047812(s+1,2) for n >= 0.  _Petros Hadjicostas_, May 31 2020
%o (PARI) {a(n)=local(M);M=matrix(n+3,n+3,r,c,if(r<c,0,if(r==0,1, polcoeff(prod(j=r+1,2*r,1q^j)/prod(j=1,r,1q^j),(r+1)*(c1), q)))); (M^2)[n+3,3]}
%Y Cf. A047812, A128567, A128568 (column 1), A128602 (row sums).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Mar 12 2007
