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A245856 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 3. 2
1, 0, 0, 20, 70, 112, 1848, 12840, 62700, 591800, 5484908, 40589276, 421291780, 4704380800, 46345716880, 533446290384, 6931113219780, 85313661653400, 1121432682942740, 16310909250477380, 237534778732260548, 3578871132644512672, 57980168196079811800 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..400

FORMULA

E.g.f.: 1/(2-exp(x)+x+x^2/2)-1/(2-exp(x)+x+x^2/2+x^3/6).

a(n) = A102233(n) - A232475(n) = A245732(n,3) - A245732(n,4).

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, 3) -b(n, 4):

seq(a(n), n=3..30);

MATHEMATICA

With[{nn=30}, CoefficientList[Series[1/(2-Exp[x]+x+x^2/2)-1/(2-Exp[x]+ x+ x^2/2+ x^3/6), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 14 2016 *)

CROSSREFS

Column k=3 of A245733.

Cf. A102233, A232475, A245732.

Sequence in context: A153728 A234367 A071395 * A053741 A303609 A052516

Adjacent sequences:  A245853 A245854 A245855 * A245857 A245858 A245859

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 04 2014

STATUS

approved

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Last modified March 26 16:58 EDT 2019. Contains 321511 sequences. (Running on oeis4.)