A026957 a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026615.

1, 6, 35, 154, 613, 2362, 9028, 34510, 132241, 508210, 1958460, 7565906, 29292820, 113633930, 441579702, 1718642278, 6698377449, 26139863330, 102125977396, 399415127682, 1563614796608, 6126581578954, 24024810462810, 94281930087290, 370254213115948, 1454967778894282

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

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

Cf. A026622, A026623, A026624, A026625, A026956, A026958, A026959.

Cf. A026960.

Programs

Magma

[1] cat [(n-1)*Binomial(2*n,n-1)*(49*n^3 -105*n^2 +62*n -24)/( 24*Binomial(2*n,4)) -2*(2*n-1): n in [2..40]]; // G. C. Greubel, Jun 17 2024

Mathematica

Table[If[n==1, 1, (n-1)*Binomial[2*n,n-1]*(49*n^3 -105*n^2 +62*n -24 )/(24*Binomial[2*n,4]) - 2*(2*n-1)], {n,40}] (* G. C. Greubel, Jun 17 2024 *)

SageMath

[1]+[(n-1)*binomial(2*n,n-1)*(49*n^3-105*n^2+62*n-24 )/( 24*binomial(2*n, 4)) -2*(2*n-1) for n in range(2,41)] # G. C. Greubel, Jun 17 2024

Formula

a(n) = (n-1)*binomial(2*n, n-1)*(49*n^3 - 105*n^2 + 62*n - 24 )/( 24*binomial(2*n, 4)) - 2*(2*n-1), for n >= 2, with a(1) = 1. - G. C. Greubel, Jun 17 2024

Extensions

More terms from Sean A. Irvine, Oct 20 2019