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A034001
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One third of triple factorial numbers.
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15
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1, 6, 54, 648, 9720, 174960, 3674160, 88179840, 2380855680, 71425670400, 2357047123200, 84853696435200, 3309294160972800, 138990354760857600, 6254565964238592000, 300219166283452416000, 15311177480456073216000
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OFFSET
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1,2
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LINKS
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FORMULA
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3*a(n) = (3*n)!!! = Product_{j=1..n} 3*j = 3^n*n!.
E.g.f.: (-1 + 1/(1-3*x))/3.
D-finite with recurrence a(n) - 3*n*a(n-1) = 0. - R. J. Mathar, Dec 02 2012
Sum_{n>=1} 1/a(n) = 3*(exp(1/3)-1).
Sum_{n>=1} (-1)^(n+1)/a(n) = 3*(1-exp(-1/3)). (End)
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MAPLE
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G(x):=(1-3*x)^(n-3): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1], x) od:x:=0:seq(f[n], n=0..16); # Zerinvary Lajos, Apr 04 2009
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MATHEMATICA
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terms = 17;
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PROG
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(GAP) List([1..20], n->3^(n-1)*Factorial(n)); # Muniru A Asiru, Jul 28 2018
(Magma) [3^(n-1)*Factorial(n): n in [1..20]]; // G. C. Greubel, Aug 15 2019
(Sage) [3^(n-1)*factorial(n) for n in (1..20)] # G. C. Greubel, Aug 15 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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