%I #23 Apr 14 2024 13:30:14
%S 4,35,252,1716,11440,75582,497420,3268760,21474180,141120525,
%T 927983760,6107086800,40225345056,265182149218,1749695026860,
%U 11554258485616,76360380541900,505037289962205,3342649210440540,22138745874816900,146721427591999680
%N a(n) = binomial(3*n-2,n+1).
%F G.f.: (3^(5/2) * cos(asin((3^(3/2) * sqrt(x))/2)/3) * x^(3/2))/(32*sin(asin((3^(3/2) * sqrt(x))/2)/3)^5 * sqrt(1-(27*x)/4)) - 1/x + 2.
%F +2*(n-2)*(2*n-3)*(n+1)*a(n) -3*(n-1)*(3*n-4)*(3*n-2)*a(n-1)=0. - _R. J. Mathar_, Jun 07 2016
%t Table[Binomial[3 n - 2, n + 1], {n, 2, 25}] (* _Vincenzo Librandi_, Aug 12 2015 *)
%o (Maxima) taylor((3^(5/2)*cos(asin((3^(3/2)*sqrt(x))/2)/3)*x^(3/2))/(32*sin(asin((3^(3/2)*sqrt(x))/2)/3)^5*sqrt(1-(27*x)/4))-1/x+2,x,0,10);
%o (PARI) vector(30, n, n++; binomial(3*n-2,n+1)) \\ _Michel Marcus_, Aug 11 2015
%o (Magma) [Binomial(3*n-2,n+1): n in [2..30]]; // _Vincenzo Librandi_, Aug 12 2015
%K nonn
%O 2,1
%A _Vladimir Kruchinin_, Aug 11 2015