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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
1, 0, 0, 0, 70, 252, 420, 660, 35640, 271700, 1389388, 5137860, 79463020, 905649500, 7336909980, 48400150764, 573924746400, 7735300382250, 85942063340210, 795156908528290, 9670781421636258, 143772253669334950, 1993964186469438950, 24015169625528033550 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 21:57 EST 2022. Contains 358453 sequences. (Running on oeis4.)