The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A245859 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A245859

Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 6.
(history; published version)

#6 by Alois P. Heinz at Mon Aug 04 13:05:23 EDT 2014

STATUS

editing

approved

#5 by Alois P. Heinz at Mon Aug 04 13:05:19 EDT 2014

FORMULA

E.g.f.: 1/(21-exp(x)+Sum_{j>=1..56} x^j/j!) - 1/(21-exp(x)+Sum_{j>=1..67} x^j/j!).

STATUS

approved

editing

#4 by Alois P. Heinz at Mon Aug 04 12:37:56 EDT 2014

STATUS

editing

approved

#3 by Alois P. Heinz at Mon Aug 04 12:37:43 EDT 2014

LINKS

Alois P. Heinz, <a href="/A245859/b245859.txt">Table of n, a(n) for n = 6..400</a>

FORMULA

a(n) = A245791(n) - A245792(n) = A245732(n,6) - A245732(n,7).

CROSSREFS

a(n) = A245791, A245792, A245732.

#2 by Alois P. Heinz at Mon Aug 04 12:35:55 EDT 2014

NAME

allocated for Alois P. Heinz

Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 6.

DATA

1, 0, 0, 0, 0, 0, 924, 3432, 6006, 10010, 16016, 24752, 17190264, 139729800, 748339320, 2910015528, 9794896188, 30251595066, 2396910064472, 33228482071400, 291616291666700, 2036218597884900, 11895959650285620, 61536913327513260, 1662981928016982300

OFFSET

6,7

FORMULA

E.g.f.: 1/(2-exp(x)+Sum_{j=1..5} x^j/j!) -1/(2-exp(x)+Sum_{j=1..6} x^j/j!).

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, 6) -b(n, 7):

seq(a(n), n=6..35);

CROSSREFS

Column k=6 of A245733.

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Aug 04 2014

STATUS

approved

editing

#1 by Alois P. Heinz at Mon Aug 04 10:47:04 EDT 2014

NAME

allocated for Alois P. Heinz

KEYWORD

allocated

STATUS

approved