A086631 Antidiagonal sums of square table A086629.

1, 2, 4, 10, 29, 92, 310, 1088, 3931, 14518, 54551, 207856, 801202, 3118532, 12239732, 48385852, 192483953, 769974110, 3095236066, 12497442266, 50660112478, 206093561590, 841151382755, 3443278744832, 14133534466258

Offset: 0

Author

Paul D. Hanna, Jul 24 2003

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001764, A086615, A086629 (table), A086630 (diagonal).

Programs

PARI

a(n) = sum(k=0, n\2, binomial(n+2*k+1, 4*k+1)*binomial(3*k, k)/(2*k+1)); \\ Seiichi Manyama, Jul 30 2023

Formula

G.f.: A(x) = 1/(1-x)^2 + x^2*A(x)^3.

a(n) = Sum_{k=0..floor(n/2)} binomial(n+2*k+1,4*k+1) * binomial(3*k,k) / (2*k+1). - Seiichi Manyama, Jul 30 2023