A060490 Number of 6-block ordered tricoverings of an unlabeled n-set.

0, 0, 120, 3030, 24552, 130740, 551640, 1997415, 6470420, 19219462, 53187840, 138658760, 343297780, 812249250, 1845669776, 4044119530, 8573706300, 17637474350, 35294157340, 68850086745, 131179071560, 244518601660, 446576824800, 800201972990, 1408466719120

Offset

1,3

Comments

A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

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} 1/(1 - y)^binomial(k, 3)*exp( -x^2/2*1/(1 - y)^n)*x^k/k!.

Crossrefs

Column k=6 of A060492.

Cf. A060094, A060484, A060491.

Sequence in context: A219834 A250651 A052721 * A158048 A219477 A183266

Adjacent sequences: A060487 A060488 A060489 * A060491 A060492 A060493

Keyword

nonn

Author

Vladeta Jovovic, Mar 20 2001

Extensions

a(1)=a(2)=0 prepended and terms a(23) and beyond from Andrew Howroyd, Jan 30 2020

Status

approved