cp's OEIS Frontend

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

%I A026616 #21 Nov 22 2024 09:29:06
%S A026616 1,3,10,34,120,434,1596,5940,22308,84370,320892,1226108,4702880,
%T A026616 18097044,69832600,270118440,1047043260,4066132050,15816664380,
%U A026616 61615392300,240347793840,938669220060,3669940053000
%N A026616 a(n) = A026615(2*n, n).
%C A026616 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
%H A026616 G. C. Greubel, <a href="/A026616/b026616.txt">Table of n, a(n) for n = 0..1000</a>
%H A026616 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>
%F A026616 From _Vladeta Jovovic_, Jan 08 2004: (Start)
%F A026616 a(n) = (1/2)*((7*n-4)/(2*n-1))*binomial(2*n, n), n >= 1.
%F A026616 G.f.: (2-x)/sqrt(1-4*x) - 1. (End)
%F A026616 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
%F A026616 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
%F A026616 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
%t A026616 Table[(7*n-4)*Binomial[2*n,n]/(4*n-2) - Boole[n==0], {n,0,30}] (* _G. C. Greubel_, Jun 13 2024 *)
%o A026616 (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
%o A026616 (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
%Y A026616 Cf. A000984, A026615, A026617, A026618, A026619, A026620, A026621.
%Y A026616 Cf. A026622, A026623, A026624, A026625, A026956, A026957, A026958.
%Y A026616 Cf. A026959, A026960.
%K A026616 nonn
%O A026616 0,2
%A A026616 _Clark Kimberling_