This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A029609 #28 Jul 02 2025 16:01:56 %S A029609 1,5,15,50,175,630,2310,8580,32175,121550,461890,1763580,6760390, %T A029609 26001500,100291500,387793800,1502700975,5834015550,22687838250, %U A029609 88363159500,344616322050,1345644686100,5260247409300,20583576819000,80619009207750,316026516094380,1239796332370260 %N A029609 Central numbers in the (2,3)-Pascal triangle A029600. %C A029609 For n > 0 also central terms of (1,4)-Pascal triangle A095666. - _Reinhard Zumkeller_, Apr 08 2012 %H A029609 Reinhard Zumkeller, <a href="/A029609/b029609.txt">Table of n, a(n) for n = 0..1000</a> %F A029609 From _Peter Bala_, Aug 16 2011: (Start) %F A029609 a(n) = (5/2)*binomial(2*n,n) for n >= 1. %F A029609 O.g.f.: -3/2+5/2*1/sqrt(1-4*x) = 1+5*x+15*x^2+50*x^3+... = 1+5*x*d/dx(log(C(x))), where C(x) is the o.g.f. for the Catalan numbers A000108. (End) %F A029609 E.g.f.: (5*exp(2*x)*BesselI(0, 2*x) - 3)/2. - _Stefano Spezia_, Feb 14 2025 %t A029609 a[n_]=(5*Binomial[2*n,n]-3KroneckerDelta[n,0])/2; Array[a,27,0] (* _Stefano Spezia_, Feb 14 2025 *) %o A029609 (Haskell) %o A029609 a029609 n = a029600 (2*n) n -- _Reinhard Zumkeller_, Apr 08 2012 %Y A029609 Cf. A000108, A029600, A095666. %K A029609 nonn,easy %O A029609 0,2 %A A029609 _Mohammad K. Azarian_ %E A029609 More terms from _James Sellers_