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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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3
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OFFSET
| 0,2
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COMMENTS
| P-recursive
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FORMULA
| 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
| a(1)=4: {123, 132} {112, 233} {113, 322} {133, 122}
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CROSSREFS
| Cf. A052502, A110105, A110106, A108242.
Sequence in context: A134908 A114498 A069120 * A024061 A067482 A013830
Adjacent sequences: A110101 A110102 A110103 * A110105 A110106 A110107
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KEYWORD
| easy,nonn
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AUTHOR
| Marni Mishna (marni.mishna(AT)inria.fr), Jul 11 2005
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