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Search: id:A110104
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| A110104 |
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a(n) is the number of coverings of 1...n by cyclic words of length 3n, such that each value from 1 to n appears precisely twice. That is, the union of all the letters in all of the words of a given covering is the multiset {1,1,2,2,...,n,n}. No repeats of words are allowed in a given covering. |
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+0
4
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| 1, 4, 3760, 23504320, 567399078400, 37518268781593600, 5543744611870143078400, 1599334510537656091623424000, 818296434784062385011283591168000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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P-recursive
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FORMULA
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Differential equation satisfied by egf: sum a(n)t^3n/(3n!) {F(0) = 1, (-2+4*t^6+16*t^3)*diff(F(t), t)+4*t^4*diff(diff(F(t), t), t)+t^2*(4+12*t^3+t^6)*F(t)} Recurrence: {a(0) = 1, (40320+328752*n+1816668*n^3+1102248*n^5+398034*n^6+1818369*n^4+1063116*n^2+78732*n^7+6561*n^8)*a(n)+(508608*n+161280+453600*n^3+34992*n^5+2916*n^6+173340*n^4+661104*n^2)*a(n+1)+(12320+19980*n+12096*n^2+3240*n^3+324*n^4)*a(n+2)-2*a(n+3), a(1) = 4, a(2) = 3760}
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EXAMPLE
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a(1)=4: {123, 132} {112, 233} {113, 322} {133, 122}
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CROSSREFS
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Cf. A052502, A110105, A110106, A108242.
Adjacent sequences: A110101 A110102 A110103 this_sequence A110105 A110106 A110107
Sequence in context: A134908 A114498 A069120 this_sequence A024061 A067482 A013830
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KEYWORD
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easy,nonn
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AUTHOR
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Marni Mishna (marni.mishna(AT)inria.fr), Jul 11 2005
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