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A230344 Number of permutations of [2n+4] in which the longest increasing run has length n+4. 3
1, 10, 137, 2360, 49236, 1209936, 34288800, 1102187520, 39656131200, 1579837754880, 69064610186880, 3288126441600000, 169388400557376000, 9389435419203840000, 557323393281887232000, 35272416767753797632000, 2371290445442664345600000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also the number of ascending runs of length n+4 in the permutations of [2n+4].

LINKS

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

FORMULA

a(n) = (n^3+10*n^2+30*n+29)*(2*n+4)!/(n+6)! for n>0, a(0) = 1.

a(n) = A008304(2*n+4,n+4) = A122843(2*n+4,n+4).

MAPLE

a:= proc(n) option remember; `if`(n<2, 1+9*n, 2*(2*n+3)*(n+2)*

      (n^3+10*n^2+30*n+29)*a(n-1)/((n+6)*(n^3+7*n^2+13*n+8)))

    end:

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

CROSSREFS

A diagonal of A008304, A122843.

Sequence in context: A096619 A276131 A003377 * A065593 A089834 A132505

Adjacent sequences:  A230341 A230342 A230343 * A230345 A230346 A230347

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 16 2013

STATUS

approved

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Last modified August 17 16:51 EDT 2017. Contains 290648 sequences.