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 A230343 Number of permutations of [2n+3] in which the longest increasing run has length n+3. 3
 1, 8, 99, 1602, 32010, 761904, 21064680, 663848640, 23500653120, 923616691200, 39914540709120, 1881558401184000, 96096062174112000, 5286518167746816000, 311689569962010240000, 19608741674518284288000, 1311187373310480906240000, 92868537238628772741120000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also the number of ascending runs of length n+3 in the permutations of [2n+3]. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..300 FORMULA a(n) = (n^3+8*n^2+20*n+19)*(2*n+3)!/(n+5)! for n>0, a(0) = 1. a(n) = A008304(2*n+3,n+3) = A122843(2*n+3,n+3). MAPLE a:= proc(n) option remember; `if`(n<2, 1+7*n, 2*(2*n+3)*(n+1)*       (n^3+8*n^2+20*n+19)*a(n-1)/((n+5)*(n^3+5*n^2+7*n+6)))     end: seq(a(n), n=0..25); CROSSREFS A diagonal of A008304, A122843. Sequence in context: A180927 A091801 A050919 * A293145 A305919 A286841 Adjacent sequences:  A230340 A230341 A230342 * A230344 A230345 A230346 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 16 2013 STATUS approved

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Last modified September 20 19:05 EDT 2019. Contains 327246 sequences. (Running on oeis4.)