A185080 a(n) = 6 * binomial(2*n,n-1) + binomial(2*n-1,n).

7, 27, 100, 371, 1386, 5214, 19734, 75075, 286858, 1100138, 4232592, 16328942, 63146500, 244711260, 950094810, 3694876515, 14390571690, 56122547250, 219140635560, 856617714810, 3351878581740, 13127747882340, 51458942047500, 201869999056206, 792497263436676

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = A046902(2*n,n) (Central terms of Clark's triangle).

a(n) = 6 * A007318(2*n,n-1) + A007318(2*n-1,n).

From G. C. Greubel, Apr 03 2024: (Start)

a(n) = (13*n+1)*A000108(n)/2.

a(n) = (2 + 22*n - 52*n^2)*a(n-1)/(12 - n - 13*n^2).

G.f.: ((6 - 11*x)*sqrt(1-4*x) - (1-4*x)*(6+x))/(2*x*(1-4*x)).

E.g.f.: (1/2)*(-1 + exp(2*x)*(BesselI(0, 2*x) + 12*BesselI(1, 2*x))).(End)

Mathematica

Table[6Binomial[2n, n-1]+Binomial[2n-1, n], {n, 30}] (* Harvey P. Dale, Dec 28 2012 *)

Prog

(Haskell)
a185080 n = 6 * a007318 (2 * n) (n - 1) + a007318 (2 * n - 1) n
(Magma) [(13*n+1)*Catalan(n)/2: n in [1..40]]; // G. C. Greubel, Apr 03 2024
(SageMath) [(13*n+1)*binomial(2*n, n)/(2*n+2) for n in range(1, 41)] # G. C. Greubel, Apr 03 2024

Crossrefs

Cf. A000108, A007318, A024482, A046224, A046902.

Sequence in context: A213588 A305653 A282642 * A006350 A054485 A090856

Adjacent sequences: A185077 A185078 A185079 * A185081 A185082 A185083

Keyword

nonn

Author

Reinhard Zumkeller, Dec 26 2012

Status

approved