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A245857 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 4. 2

%I

%S 1,0,0,0,70,252,420,660,35640,271700,1389388,5137860,79463020,

%T 905649500,7336909980,48400150764,573924746400,7735300382250,

%U 85942063340210,795156908528290,9670781421636258,143772253669334950,1993964186469438950,24015169625528033550

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

%H Alois P. Heinz, <a href="/A245857/b245857.txt">Table of n, a(n) for n = 4..400</a>

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

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

%p b:= proc(n, k) option remember; `if`(n=0, 1,

%p add(b(n-j, k)*binomial(n, j), j=k..n))

%p end:

%p a:= n-> b(n, 4) -b(n, 5):

%p seq(a(n), n=4..30);

%Y Column k=4 of A245733.

%Y Cf. A232475, A245790, A245732.

%K nonn

%O 4,5

%A _Alois P. Heinz_, Aug 04 2014

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Last modified January 30 05:55 EST 2023. Contains 359939 sequences. (Running on oeis4.)