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%I #30 Jan 07 2023 11:34:04
%S 1,15,180,1980,20790,212058,2120580,20902860,203802885,1970094555,
%T 18912907728,180532301040,1715056859880,16227076443480,
%U 152998149324240,1438182603647856,13482961909198650,126105349621328550,1176983263132399800,10964528293391303400,101970113128539121620
%N a(n) = (3^n/n!) * Product_{k=0..n-1} (3*k + 5).
%H G. C. Greubel, <a href="/A004992/b004992.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%F G.f.: (1 - 9*x)^(-5/3).
%F a(n) ~ (3/2)*Gamma(2/3)^-1*n^(2/3)*3^(2*n)*(1 + (5/9)*n^-1 - ...).
%F D-finite with recurrence: n*a(n) +3*(-3*n-2)*a(n-1)=0. - _R. J. Mathar_, Jan 17 2020
%F Sum_{n>=0} 1/a(n) = sqrt(3)*Pi/2 - 3*log(3)/2. - _Amiram Eldar_, Dec 02 2022
%p a:= n-> (3^n/n!)*mul(3*k+5, k=0..n-1): seq(a(n), n=0..25); # _G. C. Greubel_, Aug 22 2019
%t Table[9^n*Pochhammer[5/3, n]/n!, {n,0,25}] (* _G. C. Greubel_, Aug 22 2019 *)
%t Table[3^n/n! Product[3k+5,{k,0,n-1}],{n,0,20}] (* _Harvey P. Dale_, Jan 07 2023 *)
%o (PARI) a(n) = 3^n*prod(k=0,n-1, 3*k+5)/n!;
%o vector(25, n, a(n-1)) \\ _G. C. Greubel_, Aug 22 2019
%o (Magma) [1] cat [3^n*&*[3*k+5: k in [0..n-1]]/Factorial(n): n in [1..25]]; // _G. C. Greubel_, Aug 22 2019
%o (Sage) [9^n*rising_factorial(5/3, n)/factorial(n) for n in (0..25)] # _G. C. Greubel_, Aug 22 2019
%o (GAP) List([0..25], n-> 3^n*Product([0..n-1], k-> 3*k+5)/Factorial(n) ); # _G. C. Greubel_, Aug 22 2019
%Y Cf. A004988, A004989, A004990, A004991.
%K nonn,easy
%O 0,2
%A Joe Keane (jgk(AT)jgk.org)
%E Terms a(16) onward added by _G. C. Greubel_, Aug 22 2019
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