A026616 a(n) = A026615(2*n, n).

1, 3, 10, 34, 120, 434, 1596, 5940, 22308, 84370, 320892, 1226108, 4702880, 18097044, 69832600, 270118440, 1047043260, 4066132050, 15816664380, 61615392300, 240347793840, 938669220060, 3669940053000

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

If Y is a fixed 3-subset of a (2n+1)-set X then a(n) is the number of (n+1)-subsets of X intersecting Y. - Milan Janjic, Oct 28 2007

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Milan Janjic, Two Enumerative Functions

Crossrefs

Cf. A000984, A026615, A026617, A026618, A026619, A026620, A026621.

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

Cf. A026959, A026960.

Programs

Magma

[n eq 0 select 1 else ((7*n-4)*(n+1)/(4*n-2))*Catalan(n): n in [0..30]]; // G. C. Greubel, Jun 13 2024

Mathematica

Table[(7*n-4)*Binomial[2*n,n]/(4*n-2) - Boole[n==0], {n,0,30}] (* G. C. Greubel, Jun 13 2024 *)

SageMath

[(7*n-4)*binomial(2*n, n)/(4*n-2) - int(n==0) for n in range(31)] # G. C. Greubel, Jun 13 2024

Formula

From Vladeta Jovovic, Jan 08 2004: (Start)

a(n) = (1/2)*((7*n-4)/(2*n-1))*binomial(2*n, n), n >= 1.

G.f.: (2-x)/sqrt(1-4*x) - 1. (End)

E.g.f.: -1 + exp(2*x)*( (2 - x + 14*x^2)*BesselI(0, 2*x) - 13*x*BesselI(1, 2*x) - 14*x^2*BesselI(2, 2*x) ). - G. C. Greubel, Jun 13 2024

D-finite with recurrence 2*n*a(n) +3*(-3*n+2)*a(n-1) +2*(2*n-5)*a(n-2)=0. - R. J. Mathar, Nov 22 2024

D-finite with recurrence +n*(7*n-11)*a(n) -2*(7*n-4)*(2*n-3)*a(n-1)=0. - R. J. Mathar, Nov 22 2024