A026959 a(n) = Sum_{k=0..n-3} T(n,k) * T(n,k+3), with T given by A026615.

1, 14, 115, 640, 3049, 13494, 57491, 239768, 986976, 4027666, 16335660, 65955960, 265386251, 1064993622, 4264898875, 17051078256, 68080259516, 271537515786, 1082098938452, 4309269809044, 17151303222746, 68232856509950, 271350536990740, 1078796298028680, 4287906741748940

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000

Crossrefs

Cf. A026615, A026616, A026617, A026618, A026619, A026620, A026621.

Cf. A026622, A026623, A026624, A026625, A026956, A026957, A026958.

Cf. A026960.

Programs

Magma

[n eq 3 select 1 else Binomial(2*n,n+3)*(49*n^4 -154*n^3 +279*n^2 -390*n +288)/(24* Binomial(2*n,4)) -(n-2)*(2*n^2-5*n+9)/3: n in [3..40]]; // G. C. Greubel, Jun 17 2024

Mathematica

Table[(2*n-4)!*(49*n^4 -154*n^3 +279*n^2 -390*n +288)/((n-3)!*(n+3)!) - (n-2)*(2*n^2-5*n+9)/3 +Boole[n==3], {n,3,40}] (* G. C. Greubel, Jun 17 2024 *)

SageMath

[binomial(2*n,n+3)*(49*n^4 -154*n^3 +279*n^2 -390*n +288)/(24*binomial(2*n,4)) -(1/3)*(n-2)*(2*n^2-5*n+9) +int(n==3) for n in range(3,41)] # G. C. Greubel, Jun 17 2024

Formula

a(n) = binomial(2*n, n+3)*(49*n^4 - 154*n^3 + 279*n^2 - 390*n + 288)/(4! * binomial(2*n, 4)) - (1/3)*(n-2)*(2*n^2 - 5*n + 9) + [n=3]. - G. C. Greubel, Jun 17 2024

Extensions

More terms from Sean A. Irvine, Oct 20 2019