A086631 - OEIS

%I #12 Jul 30 2023 09:45:24

%S 1,2,4,10,29,92,310,1088,3931,14518,54551,207856,801202,3118532,

%T 12239732,48385852,192483953,769974110,3095236066,12497442266,

%U 50660112478,206093561590,841151382755,3443278744832,14133534466258

%N Antidiagonal sums of square table A086629.

%H Seiichi Manyama, <a href="/A086631/b086631.txt">Table of n, a(n) for n = 0..1000</a>

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

%F 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

%o (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

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 24 2003