Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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