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A024487 a(n) = (1/(4n+2))*M(3n; n,n,n).

%I A024487 #22 Aug 05 2024 06:28:40
%S A024487 1,9,120,1925,34398,659736,13302432,278397405,5996669250,132166590270,
%T A024487 2967978162240,67694635250424,1564409223571600,36561597688116000,
%U A024487 862822254602816640,20535537339485077005,492426552811873991850,11886753074132473787250,288645723487776840570000
%N A024487 a(n) = (1/(4n+2))*M(3n; n,n,n).
%C A024487 Number of standard Young tableaux of shape (n,n,{1}^n). - _Alois P. Heinz_, Apr 05 2013
%H A024487 Alois P. Heinz, <a href="/A024487/b024487.txt">Table of n, a(n) for n = 1..250</a>
%F A024487 a(n) ~ 3^(3*n+1/2) / (8*Pi*n^2). - _Vaclav Kotesovec_, Sep 06 2014
%F A024487 a(n) = A006480(n) / (4*n + 2) if n>0. - _Michael Somos_, Oct 25 2014
%F A024487 D-finite with recurrence: n^2*(2*n+1)*a(n) -3*(3*n-1)*(2*n-1)*(3*n-2)*a(n-1)=0. - _R. J. Mathar_, Apr 27 2020
%e A024487 G.f. = x + 9*x^2 + 120*x^3 + 1925*x^4 + 34398*x^5 + 659736*x^6 + ...
%p A024487 with(combinat):
%p A024487 a:= n-> multinomial(3*n, n$3)/(4*n+2):
%p A024487 seq(a(n), n=1..30);  # _Alois P. Heinz_, Apr 05 2013
%t A024487 a[ n_] := If[ n < 1, 0, (3 n)! / (n!^3 (4 n + 2))]; (* _Michael Somos_, Oct 25 2014 *)
%o A024487 (PARI) {a(n) = if( n<1, 0, (3*n)! / (n!^3 * (4*n + 2)))}; /* _Michael Somos_, Oct 25 2014 */
%Y A024487 Cf. A006480.
%K A024487 nonn,easy
%O A024487 1,2
%A A024487 _Clark Kimberling_
%E A024487 Corrected and extended by _Alois P. Heinz_, Apr 05 2013