A026618 a(n) = A026618(2*n, n-2).

1, 11, 50, 212, 870, 3509, 14014, 55640, 220116, 868870, 3425092, 13491064, 53117350, 209097945, 823111350, 3240499440, 12759776700, 50254414650, 197979380220, 780170359800, 3075303389340

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A026615, A026616, A026617, A026619, A026620, A026621, A026622.

Cf. A026623, A026624, A026625, A026956, A026957, A026958, A026959.

Cf. A026960.

Programs

Magma

[n eq 2 select 1 else (7*n^2-4*n+4)*Binomial(2*n,n-2)/(2*Binomial(2*n,2)): n in [2..40]]; // G. C. Greubel, Jun 13 2024

Mathematica

Table[(7*n^2-4*n+4)*Binomial[2*n,n-2]/(2*Binomial[2*n,2]) -Boole[n==2], {n,2,40}] (* G. C. Greubel, Jun 13 2024 *)

SageMath

[(7*n^2-4*n+4)*binomial(2*n, n-2)/(2*binomial(2*n, 2)) - int(n==2) for n in range(2,41)] # G. C. Greubel, Jun 13 2024

Formula

From G. C. Greubel, Jun 13 2024: (Start)

a(n) = (7*n^2 - 4*n + 4)*binomial(2*n, n-2)/(2*binomial(2*n, 2)) -[n=2].

G.f.: ( (2 - 9*x + 8*x^2 - 2*x^3) - (2 - 5*x + 2*x^2 + 2*x^4)*sqrt(1 - 4*x) )/(2*x^2*sqrt(1-4*x)).

E.g.f.: exp(2*x)*( (3 - x)*BesselI(0, 2*x) + (x - 1 - 2/x)*BesselI(1, 2*x) ) - (1 + x^2/2). (End)