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A004989
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a(n) = (3^n/n!) * Product_{k=0..n-1} (3*k - 2).
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6
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1, -6, -9, -36, -189, -1134, -7371, -50544, -360126, -2640924, -19806930, -151252920, -1172210130, -9197341020, -72921775230, -583374201840, -4703454502335, -38180983607190, -311811366125385, -2560135427134740, -21121117273861605, -175003543126281870, -1455711290550435555
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ -(2/3)*Gamma(1/3)^-1*n^(-5/3)*3^(2*n)*(1 + (5/9)*n^-1 + ...).
G.f.: (1-9*x)^(2/3).
D-finite with recurrence: n*a(n) +3*(-3*n+5)*a(n-1)=0. - R. J. Mathar, Jan 17 2020
Sum_{n>=0} 1/a(n) = 99/128 - 5*sqrt(3)*Pi/512 - 15*log(3)/512. - Amiram Eldar, Dec 02 2022
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MAPLE
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a:= n-> (3^n/n!)*product(3*k-2, k=0..n-1); seq(a(n), n=0..25); # G. C. Greubel, Aug 22 2019
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MATHEMATICA
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Table[9^n*Pochhammer[-2/3, n]/n!, {n, 0, 25}] (* G. C. Greubel, Aug 22 2019 *)
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PROG
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(PARI) a(n)=if(n<0, 0, prod(k=0, n-1, 3*k-2)*3^n/n!)
(Magma) [1] cat [3^n*(&*[3*k-2: k in [0..n-1]])/Factorial(n): n in [1..25]]; // G. C. Greubel, Aug 22 2019
(Sage) [9^n*rising_factorial(-2/3, n)/factorial(n) for n in (0..25)] # G. C. Greubel, Aug 22 2019
(GAP) List([0..25], n-> 3^n*Product([0..n-1], k-> 3*k-2)/Factorial(n) ); # G. C. Greubel, Aug 22 2019
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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Joe Keane (jgk(AT)jgk.org)
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STATUS
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approved
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