A245860 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 7.

1, 0, 0, 0, 0, 0, 0, 3432, 12870, 22880, 38896, 63648, 100776, 155040, 399305520, 3292693008, 17879790324, 70676513424, 242216077400, 762341522800, 2264840592300, 478970960616720, 6869326015894680, 61426122596911800, 435982960069722000, 2589856033041531072

Offset

7,8

Links

Alois P. Heinz, Table of n, a(n) for n = 7..400

Formula

E.g.f.: 1/(1-Sum_{j>=7} x^j/j!) - 1/(1-Sum_{j>=8} x^j/j!).

a(n) = A245792(n) - A245793(n) = A245732(n,7) - A245732(n,8).

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, 7) -b(n, 8):
seq(a(n), n=7..35);

Crossrefs

Column k=7 of A245733.

Cf. A245792, A245793, A245732.

Sequence in context: A290290 A024751 A024759 * A177307 A140911 A351486

Adjacent sequences: A245857 A245858 A245859 * A245861 A245862 A245863

Keyword

nonn

Author

Alois P. Heinz, Aug 04 2014

Status

approved