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Search: id:A084915
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| 0, 1, 8, 108, 2304, 72000, 3110400, 177811200, 13005619200, 1185137049600, 131681894400000, 17526860144640000, 2753310393630720000, 504085244567224320000
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OFFSET
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0,3
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COMMENT
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Used to prove that sum{n=1,oo,1/A002378(n)}=1. Examining sum{n=1,k,1/A002378(n)} gives 1/2, 1/2+1/6, 1/2+1/6+1/12. Simplifying gives 1/2, 8/12, 108/144, where the numerators are this sequence and the denominators are A010790. Therefore we have k!^2*k/k!(k+1)! = k*k!/(k+1)!=k/(k+1), which tends to 1 as k tends to infinity.
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FORMULA
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n!(n+1)!-n!^2
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EXAMPLE
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a(3)=3!^2*3=36*3=108
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MAPLE
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seq(add((count(Permutation(k)))^2, k=1..n), n=0..13); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 17 2006
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PROGRAM
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(PARI) for(n=1, 50, print1(n!^2*n", "))
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CROSSREFS
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Cf. A002378, A010790.
Sequence in context: A048543 A120975 A099699 this_sequence A138456 A095917 A098623
Adjacent sequences: A084912 A084913 A084914 this_sequence A084916 A084917 A084918
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Jul 14 2003
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