A245862 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 9.

1, 0, 0, 0, 0, 0, 0, 0, 0, 48620, 184756, 335920, 587860, 994840, 1634380, 2615008, 4085950, 6249100, 227882805150, 1914150638400, 10597377540750, 42894094729200, 150967391072550, 488846715676800, 1495608303532200, 4389524294884872, 12479799500904120

Offset

9,10

Links

Alois P. Heinz, Table of n, a(n) for n = 9..400

Formula

E.g.f.: 1/(1-Sum_{j>=9} x^j/j!) - 1/(1-Sum_{j>=10} x^j/j!).

a(n) = A245794(n) - A245795(n) = A245732(n,9) - A245732(n,10).

Maple

b:= proc(n, k) option remember; `if`(n=0, 1,
      add(b(n-j, k)*binomial(n, j), j=k..n))
    end:
a:= n-> b(n, 9) -b(n, 10):
seq(a(n), n=9..40);

Crossrefs

Column k=9 of A245733.

Cf. A245794, A245795, A245732.

Sequence in context: A268852 A024753 A024761 * A177313 A140924 A351488

Adjacent sequences: A245859 A245860 A245861 * A245863 A245864 A245865

Keyword

nonn

Author

Alois P. Heinz, Aug 04 2014

Status

approved