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A230251 Number of permutations of [2n+1] in which the longest increasing run has length n+1. 3
1, 4, 41, 602, 11304, 257400, 6881160, 211170960, 7315701120, 282398538240, 12019910112000, 559278036979200, 28242651241728000, 1538394175334016000, 89912239244860032000, 5612575361948755200000, 372687441873534627840000, 26231028469670851706880000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also the number of ascending runs of length n+1 in the permutations of [2n+1].

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

FORMULA

a(n) = A008304(2*n+1,n+1) = A122843(2*n+1,n+1).

For n>0, a(n) = (5+6*n+4*n^2+n^3)*(2*n+1)!/(n+3)!. - Vaclav Kotesovec, Oct 15 2013

MAPLE

a:= proc(n) option remember; `if`(n<2, 1+3*n,

      2*n*(2*n+1)*(n^3+4*n^2+6*n+5)*a(n-1)/((n+3)*(n^3+n^2+n+2)))

    end:

seq(a(n), n=0..25);

MATHEMATICA

Flatten[{1, Table[(5+6*n+4*n^2+n^3)*(2*n+1)!/(n+3)!, {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 15 2013 *)

CROSSREFS

Diagonal of A008304, A122843.

Sequence in context: A064327 A134277 A085340 * A001908 A270703 A192547

Adjacent sequences:  A230248 A230249 A230250 * A230252 A230253 A230254

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 13 2013

STATUS

approved

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Last modified June 28 23:44 EDT 2017. Contains 288852 sequences.