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A110103
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a(n) is the number of 2-regular 4-hypergraphs on 2n labeled vertices. (In a r-hypergraph, each hyper-edge is a proper r-set; k-regular implies that each vertex is in exactly k hyperedges.)
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1
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1, 0, 0, 15, 1855, 469980, 214402650, 160081596675, 182667234224475, 302414315250247200, 697372026302486234700, 2167773244010692751057625, 8842276105055583472501844625, 46275602006744820263447546152500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| P-recursive
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LINKS
| Marni Mishna, Maple worksheet
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FORMULA
| Differential equation satisfied by exponential generating function sum a(n) t^(2n)/(2n)! {F(0) = 1, -144*t^3*(-2 + t^2)^2*diff(diff(F(t), t), t)-12*(-2 + t^2)*(2*t^8-t^6 + 72 + 6*t^4-108*t^2)*diff(F(t), t)-t^5*(-2 + t^2)*(t^2-3)*(t^4 + 4*t^2 + 36)*F(t)}
Linear recurrence for a(n): {(15067980*n + 10550232*n^6 + 2859384*n^7 + 522720*n^8 + 128*n^11 + 2494800 + 61600*n^9 + 4224*n^10 + 52629038*n^3 + 45995730*n^4 + 26679070*n^5 + 37729494*n^2)*a(n) + (3791790*n + 109368*n^6 + 13872*n^7 + 1008*n^8 + 1247400 + 32*n^9 + 3747208*n^3 + 1767087*n^4 + 543858*n^5 + 4994577*n^2)*a(n + 1) + (28354500*n + 154560*n^6 + 11712*n^7 + 384*n^8 + 15478428*n^3 + 5309976*n^4 + 1152480*n^5 + 27874680*n^2 + 12474000)*a(n + 2) + (-623700-794025*n-48*n^6-115380*n^3-17760*n^4-1440*n^5-416757*n^2)*a(n + 3) + (599130*n + 534600 + 267282*n^2 + 59328*n^3 + 6552*n^4 + 288*n^5)*a(n + 4) + (-14166*n-26730-2484*n^2-144*n^3)*a(n + 5) + 54*a(n + 6), a(3) = 15, a(4) = 1855, a(5) = 469980, a(0) = 1, a(1) = 0, a(2) = 0}
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EXAMPLE
| One of the 15 2-regular 4-hypergraphs on 6 vertices: {{1234},{4561}, {2356}}
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CROSSREFS
| Cf. A025035, A110100, A110101, A025036.
Sequence in context: A205346 A070862 A077730 * A199098 A126681 A200797
Adjacent sequences: A110100 A110101 A110102 * A110104 A110105 A110106
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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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