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 A217324 Number of self-inverse permutations in S_n with longest increasing subsequence of length 4. 2
 1, 4, 19, 69, 265, 929, 3356, 11626, 41117, 142206, 499836, 1734328, 6099193, 21282265, 75125770, 263906332, 936517637, 3313246237, 11827430209, 42139231729, 151339387003, 542857007499, 1961171657524, 7079621540798, 25720257983591, 93396276789196 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 COMMENTS Also the number of Young tableaux with n cells and 4 rows. LINKS Alois P. Heinz, Table of n, a(n) for n = 4..1000 FORMULA a(n) = A182172(n,4)-A182172(n,3) = A005817(n)-A001006(n). EXAMPLE a(4) = 1: 1234. a(5) = 4: 12354, 12435, 13245, 21345. a(6) = 19: 123654, 124365, 125436, 125634, 126453, 132465, 132546, 143256, 145236, 153426, 163452, 213465, 213546, 214356, 321456, 341256, 423156, 523416, 623451. MAPLE a:= proc(n) option remember; `if`(n<4, 0, `if`(n=4, 1,       ((2+n)*(30*n^5+199*n^4-374*n^3-1537*n^2-406*n+408)*a(n-1)        -4*(n-1)*(n-2)*(120*n^4+46*n^3-471*n^2+371*n+204)*a(n-3)        +(n-1)*(285*n^5-262*n^4-2755*n^3-1520*n^2+820*n-48)*a(n-2)        -48*(n-1)*(n-3)*(3*n+7)*(5*n+4)*(n-2)^2*a(n-4))/       ((n-4)*(5*n-1)*(3*n+4)*(n+4)*(n+3)*(n+2))))     end: seq(a(n), n=4..40); CROSSREFS Column k=4 of A047884. Cf. A001006, A005817, A182172. Sequence in context: A000306 A100185 A291888 * A129019 A167247 A267192 Adjacent sequences:  A217321 A217322 A217323 * A217325 A217326 A217327 KEYWORD nonn,easy AUTHOR Alois P. Heinz, Sep 30 2012 STATUS approved

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Last modified October 18 03:25 EDT 2019. Contains 328135 sequences. (Running on oeis4.)