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 A241193 a(n) = Sum_{k=1..n} ((3*n-k-1)/(2*n-k))*(3*n-k-2)!/((n-1)!*(n-1)!*(n-k)!). 1
 1, 11, 181, 3499, 73501, 1623467, 37081045, 867484331, 20661914989, 499049420011, 12188943245909, 300438089843371, 7461880085538581, 186524863637339819, 4688354828111460181, 118407620161890380459, 3002994055439841324301, 76441823131542496027499, 1952230701520399696996501, 50003999526279431605603499 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of atomic permutations with three runs of equal length n. LINKS C. J. Fewster, D. Siemssen, Enumerating Permutations by their Run Structure, arXiv preprint arXiv:1403.1723 [math.CO], 2014. FORMULA Conjecture: -(2*n-1)*(n-1)^2*a(n) +2*(32*n^3-131*n^2+187*n-94)*a(n-1) +3*(-86*n^3+721*n^2-1896*n+1617)*a(n-2) -18*(2*n-5)*(3*n-8)*(3*n-7)*a(n-3)=0. - R. J. Mathar, Aug 26 2014 MAPLE A241193:=n->add( ((3*n-k-1)/(2*n-k))*(3*n-k-2)!/((n-1)!*(n-1)!*(n-k)!), k=1..n); [seq(A241193(n), n=1..40)]; MATHEMATICA a[n_] := Sum[((3n-k-1)/(2n-k))(3n-k-2)!/((n-1)! (n-1)! (n-k)!), {k, 1, n}]; Array[a, 20] (* Jean-François Alcover, Oct 08 2018 *) PROG (PARI) a(n) = sum(k=1, n, ((3*n-k-1)/(2*n-k))*(3*n-k-2)!/((n-1)!*(n-1)!*(n-k)!)); CROSSREFS Sequence in context: A020456 A036935 A205088 * A143413 A009118 A321848 Adjacent sequences:  A241190 A241191 A241192 * A241194 A241195 A241196 KEYWORD nonn AUTHOR N. J. A. Sloane, Apr 26 2014 STATUS approved

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Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)