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%I #21 Sep 27 2022 09:22:56
%S 1,9,216,9720,699840,73483200,10581580800,1999918771200,
%T 479980505088000,142554210011136000,51319515604008960000,
%U 22016072194119843840000,11096100385836401295360000,6491218725714294757785600000,4362098983680006077231923200000
%N a(n) = 3^n*n!*(n+2)!/2!.
%H Harry J. Smith, <a href="/A064633/b064633.txt">Table of n, a(n) for n = 0..75</a>
%F Hypergeometric g.f.: (1-3*x)^(-3).
%F a(0)=1, a(n) = n!*subs(x=0, (d^n/dx^n)(-1/((3*x-1)^3))), n = 1, 2, ...
%F From _Amiram Eldar_, Sep 27 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 6*BesselI(2,2/sqrt(3)).
%F Sum_{n>=0} (-1)^n/a(n) = 6*BesselJ(2,2/sqrt(3)). (End)
%t Table[3^n n! (n+2)!/2,{n,0,20}] (* _Harvey P. Dale_, Feb 25 2015 *)
%o (PARI) { for (n=0, 75, write("b064633.txt", n, " ", 3^n*n!*(n + 2)!/2) ) } \\ _Harry J. Smith_, Sep 20 2009
%Y Cf. A000244, A010791.
%K nonn
%O 0,2
%A _Karol A. Penson_, Oct 01 2001
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