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

1,2

Links

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

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

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 *)

Prog

(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
(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

Crossrefs

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

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

Cf. A026960.

Sequence in context: A027985 A078799 A203288 * A026987 A375248 A030532

Adjacent sequences: A026954 A026955 A026956 * A026958 A026959 A026960

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 20 2019

Status

approved