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%I #19 Jan 06 2019 04:07:07
%S 3,6,19,65,231,840,3102,11583,43615,165308,629850,2410226,9256534,
%T 35659200,137733660,533216475,2068423695,8037976980,31285334850,
%U 121941160110,475898730450
%N a(n) = binomial(2n, n) + binomial(2n-1, n-1) + binomial(2n+1, n).
%H Robert Israel, <a href="/A184937/b184937.txt">Table of n, a(n) for n = 0..1661</a>
%F a(n) = A000984(n) + A088218(n) + A088218(n+1). - _R. J. Mathar_, Feb 04 2011
%F From _Robert Israel_, Jan 05 2019: (Start)
%F G.f.: 1/2 - 1/(2*x) + (1+3*x)/(2*x*sqrt(1-4*x)).
%F (6 + 12*n)*a(n) + (7 + n)*a(1 + n) + (-3 - n)*a(n + 2) = 0. (End)
%p A184937 := proc(n) binomial(2*n,n)+binomial(2*n-1,n-1)+binomial(2*n+1,n) ; end proc: # _R. J. Mathar_, Jan 04 2011
%t Table[Binomial[2 n, n] + Binomial[2 n - 1, n - 1] + Binomial[2 n + 1, n], {n, 0, 20}]
%K nonn
%O 0,1
%A _Jon Perry_, Feb 02 2011
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