A125807 Central terms of odd-indexed rows of triangle A125806: a(n) = A125806(2n+1,n).

1, 3, 16, 119, 1070, 10762, 116546, 1330923, 15823388, 194168612, 2444224858, 31422225930, 411141476444, 5460849893348, 73474839110524, 999764999592077, 13738614091375204, 190450074950481408, 2660727794475865450

Offset: 0

Author

Paul D. Hanna, Dec 12 2006

Keywords

• nonn

Comments

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).

Crossrefs

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

Programs

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)}