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A026616
a(n) = A026615(2*n, n).
16
1, 3, 10, 34, 120, 434, 1596, 5940, 22308, 84370, 320892, 1226108, 4702880, 18097044, 69832600, 270118440, 1047043260, 4066132050, 15816664380, 61615392300, 240347793840, 938669220060, 3669940053000
OFFSET
0,2
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
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
MATHEMATICA
Table[(7*n-4)*Binomial[2*n, n]/(4*n-2) - Boole[n==0], {n, 0, 30}] (* G. C. Greubel, Jun 13 2024 *)
PROG
(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
(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
KEYWORD
nonn
STATUS
approved