A136631 Antidiagonal sums of triangle A136630, omitting antidiagonals of all zeros.

1, 1, 2, 6, 28, 177, 1449, 14869, 185230, 2738962, 47287352, 939759621, 21241309681, 540698975061, 15370957337418, 484433735633218, 16817886069720724, 639545680226171989, 26507567678760284105

Offset: 0

Author

Paul D. Hanna, Jan 14 2008

Keywords

• nonn

Crossrefs

Cf. A136630, A003724 (row sums of A136630).

Programs

PARI

{a(n)=sum(k=0,n,polcoeff(1/prod(j=0,k\2,1-(2*j+(k%2))^2*x^2 +x*O(x^(2*n-2*k))),2*n-2*k))}

Formula

a(n) = Sum_{k=0..n} [x^(2n-2k)] Product_{j=0..[k/2]} 1/(1 - (2j + k-2[k/2])^2*x^2).