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%I #17 Sep 08 2022 08:46:06
%S 1,1,5,7,42,66,429,715,4862,8398,58786,104006,742900,1337220,9694845,
%T 17678835,129644790,238819350,1767263190,3282060210,24466267020,
%U 45741281820,343059613650,644952073662,4861946401452,9183676536076,69533550916004
%N a(n) = binomial(2*(n+1),n) * gcd(n,2)/(2*(n+1)).
%C This gives the next-to-central entries of the even-indexed rows of the triangle A107711.
%C For the central entries (of the even-numbered rows) see A001700.
%C This sequence is composed of the bisection sequences A024492 (even part) and A065097 (odd part).
%H Vincenzo Librandi, <a href="/A234040/b234040.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = binomial(2*(n+1),n)*gcd(n,2)/(2*(n+1)) for n >= 0.
%F a(n) = A107711(2*(n+1), n) for n >= 0.
%F G.f.: (3*c(x)- c(-x)-2)/(4*x) =(4*(1-x) - 3*sqrt(1-4*x) - sqrt(1+4*x))/(8*x^2), with c(x) the o.g.f. of the Catalan numbers A000108. See the bisection comment above.
%t Table[Binomial[2 (n + 1), n] GCD[n, 2]/(2 (n + 1)), {n, 0, 40}] (* _Vincenzo Librandi_, Feb 25 2014 *)
%o (Magma) [Binomial(2*(n+1),n)*Gcd(n,2)/(2*(n+1)): n in [0..30]]; // _Vincenzo Librandi_, Feb 25 2014
%Y Cf. A000108, A024492, A065097, A107711.
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_, Feb 23 2014
%E a(26) from _Vincenzo Librandi_, Feb 25 2014
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