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%I #11 May 31 2020 22:10:08
%S 1,6,31,133,587,2531,10950,47185,203704,879711,3804530,16464710,
%T 71312805,309083291,1340546867,5817555402,25258769216,109711224970,
%U 476675868834,2071569641859,9004430215111,39144480326143,170184867215647,739924236443359,3217001700174226
%N Column 1 of triangle A128567.
%C A128567 is the matrix square of Parker's partition triangle A047812.
%F a(n) = Sum_{s=1..n+1} A047812(n+2,s)*A047812(s+1,1) = Sum_{s=1..n+1} A047812(n+2,s)*A007042(s+1) for n >= 0. - _Petros Hadjicostas_, May 31 2020
%o (PARI) {a(n)=local(M);M=matrix(n+2,n+2,r,c,if(r<c,0,if(r==0,1, polcoeff(prod(j=r+1,2*r,1-q^j)/prod(j=1,r,1-q^j),(r+1)*(c-1), q)))); (M^2)[n+2,2]}
%Y Cf. A007042, A047812, A128567, A128569 (column 2), A128602 (row sums).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Mar 12 2007
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