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A141052
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Number of runs or rising sequences of length 2 among all permutations of n.
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0
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1, 4, 21, 130, 930, 7560, 68880, 695520, 7711200, 93139200, 1217462400, 17124307200, 257902444800, 4140968832000, 70614415872000, 1274546617344000, 24275666967552000, 486580401635328000, 10238462617743360000, 225651661258383360000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| Column 2 of A122843
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REFERENCES
| C. M. Grinstead and J. L. Snell, Introduction to Probability, American Mathematical Society, 1997, pp.120-131.
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LINKS
| Persi Diaconis, Mathematical developments from the analysis of riffle shuffling, p. 4.
Francis Edward Su, Rising Sequences in Card Shuffling
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FORMULA
| a[n]=n!(5n+1)/4!+Floor[2/n](1/12), n>=2 Recurrence: a[2]=1; a[3]=4; a[n]=(n +1)a[n-1]+(n-1)!/6, n>=2 E.f.g.: (x^3 (11x-16))/(24 (x-1)^2)
a[n]=n!(5n+1)/4!+Floor[2/n](1/12), n>=2
Recurrence: a[2]=1; a[3]=4; a[n]=(n +1)a[n-1]+(n-1)!/6, n>=2
E.f.g.: (x^3 (16-11x))/(24 (x-1)^2)
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EXAMPLE
| a[2]=4 because of the 6 permutations of n=3, there are 4 rising sequences of length 2:
{1,2} in {1,2,3}
{1,2} in {1,3,2}
{2,3} in {2,3,1}
{1,2} in {3,1,2}
a[2]=4 because of the 6 permutations of n=3, there are 4 rising sequences of length 2:
{1,2} in {1,3,2}
{2,3} in {2,1,3}
{2,3} in {2,3,1}
{1,2} in {3,1,2}
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MATHEMATICA
| Table[n!(5n + 1)/4! + Floor[2/n](1/12), {n, 2, 10}]
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CROSSREFS
| Cf. cf. A122843, A008292, A097900, A001286, A001048, A000142, A028387, A001710.
Cf. A122843, A008292, A097900, A001286, A001048, A000142, A028387, A001710.
Sequence in context: A007345 A099250 A111177 * A058308 A078591 A090366
Adjacent sequences: A141049 A141050 A141051 * A141053 A141054 A141055
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KEYWORD
| easy,nonn
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AUTHOR
| Harlan J. Brothers (harlan(AT)brotherstechnology.com), Jul 31 2008, Aug 24 2008
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