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

3,2

Links

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

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

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 *)

Prog

(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
(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

Crossrefs

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

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

Cf. A026960.

Sequence in context: A076429 A027204 A200037 * A026989 A204240 A178258

Adjacent sequences: A026956 A026957 A026958 * A026960 A026961 A026962

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 20 2019

Status

approved