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Search: id:A060490
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| A060490 |
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Number of 6-block ordered tricoverings of an unlabeled n-set. |
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+0
3
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| 120, 3030, 24552, 130740, 551640, 1997415, 6470420, 19219462, 53187840, 138658760, 343297780, 812249250, 1845669776, 4044119530, 8573706300, 17637474350, 35294157340, 68850086745, 131179071560, 244518601660
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OFFSET
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3,1
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COMMENT
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A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering.
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FORMULA
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a(n)=binomial(n + 19, 19) - 6*binomial(n + 9, 9) - 15*binomial(n + 7, 7) + 135*binomial(n + 3, 3) - 310*binomial(n + 1, 1) + 240*binomial(n, 0) - 45*binomial(n - 1, - 1); G.f.: - y^3*( - 78600*y^3 + 271080*y^4 - 120 - 630*y + 13248*y^2 - 635805*y^5 + 4300*y^15 - 15840*y^14 + 32760*y^13 - 18240*y^12 - 114120*y^11 + 442800*y^10 - 915315*y^9 - 1371804*y^7 + 1305540*y^8 + 1081360*y^6 + 45*y^17 - 660*y^16)/( - 1 + y)^20; E.g.f. for ordered k - block tricoverings of an unlabeled n - set is exp( - x + x^2/2 + x^3/3*y/(1 - y))*Sum_{k=0..inf}1/(1 - y)^binomial(k, 3)*exp( - x^2/2*1/(1 - y)^n)*x^k/k!.
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CROSSREFS
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Cf. A006095, A060483-A060492, A060090-A060095, A060069, A060070, A060051-A060053, A002718, A059443, A003462, A059945-A059951.
Sequence in context: A126232 A105943 A052721 this_sequence A052722 A139389 A000514
Adjacent sequences: A060487 A060488 A060489 this_sequence A060491 A060492 A060493
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 20 2001
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