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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
OFFSET
3,4
LINKS
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.
Sequence in context: A362053 A357921 A335557 * A053741 A303609 A052516
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 04 2014
STATUS
approved