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Central terms of odd-indexed rows of triangle A125806: a(n) = A125806(2n+1,n).
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%I #3 Mar 30 2012 18:37:02

%S 1,3,16,119,1070,10762,116546,1330923,15823388,194168612,2444224858,

%T 31422225930,411141476444,5460849893348,73474839110524,

%U 999764999592077,13738614091375204,190450074950481408,2660727794475865450

%N Central terms of odd-indexed rows of triangle A125806: a(n) = A125806(2n+1,n).

%C Central terms of even-indexed rows of triangle A125806 equal A063075 (number of partitions of 2n^2 whose Ferrers-plot fits within a 2n X 2n box and cover an n X n box).

%o (PARI) {a(n)=local(C_q=if(n==0,1,prod(j=n+2,2*n+1,1-q^j)/prod(j=1,n,1-q^j))); sum(i=0,(n+1)*n,polcoeff(C_q,i)^2)}

%Y Cf. A125806 (triangle); A063075; A125808, A125809 (row sums).

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 12 2006