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Search: id:A126074
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| A126074 |
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Triangle read by rows: T(n,k) is the number of permutations of n elements that have the longest cycle length k. |
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| 1, 1, 1, 1, 3, 2, 1, 9, 8, 6, 1, 25, 40, 30, 24, 1, 75, 200, 180, 144, 120, 1, 231, 980, 1260, 1008, 840, 720, 1, 763, 5152, 8820, 8064, 6720, 5760, 5040
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Sum of the n-th row is the number of all permutations of n elements: Sum_{k=1..n, T(n,k)} = n! = A000142(n) We can extend T(n,k)=0, if k<=0 or k>n.
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LINKS
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IBM Research : Ponder This
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FORMULA
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T(n,1) = 1 T(n,2) = n! * Sum_{k=1..[n/2], (1/(k! * (2!)^k * (n-2k)!)} T(n,k) = n!/k * (1-1/(n-k)-...-1/(k+1)-1/2k), if n/3 < k <= n/2 T(n,k) = n!/k, if n/2 < k <= n T(n,n) = (n-1)! = A000142(n-1)
E.g.f. for k-th column: exp(-x^k*LerchPhi(x,1,k))*(exp(x^k/k)-1)/(1-x). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 03 2007
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CROSSREFS
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Cf. A000142.
Cf. A071007, A080510.
Sequence in context: A109267 A108073 A057731 this_sequence A108916 A119421 A121581
Adjacent sequences: A126071 A126072 A126073 this_sequence A126075 A126076 A126077
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KEYWORD
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base,nonn,tabl
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AUTHOR
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Dan Dima (dimad72(AT)gmail.com), Mar 01 2007
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