A245857 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 4.

1, 0, 0, 0, 70, 252, 420, 660, 35640, 271700, 1389388, 5137860, 79463020, 905649500, 7336909980, 48400150764, 573924746400, 7735300382250, 85942063340210, 795156908528290, 9670781421636258, 143772253669334950, 1993964186469438950, 24015169625528033550

Offset

4,5

Links

Alois P. Heinz, Table of n, a(n) for n = 4..400

Formula

E.g.f.: 1/(1-Sum_{j>=4} x^j/j!) - 1/(1-Sum_{j>=5} x^j/j!).

a(n) = A232475(n) - A245790(n) = A245732(n,4) - A245732(n,5).

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, 4) -b(n, 5):
seq(a(n), n=4..30);

Crossrefs

Column k=4 of A245733.

Cf. A232475, A245790, A245732.

Sequence in context: A235303 A234564 A234557 * A227879 A072596 A309310

Adjacent sequences: A245854 A245855 A245856 * A245858 A245859 A245860

Keyword

nonn

Author

Alois P. Heinz, Aug 04 2014

Status

approved