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 A263408 Triangle read by rows: T(n>=1, k>=0) is the number of standard tableaux of size n and (Haglund and Stevens) inversion number k. 0
 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 3, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS Row sums give A000085, n >= 2. The inversion number is the total number of inversion pairs for the tableau. An inversion pair is defined as a pair of cells (a,b), (x,y) such that the content of (x,y) is greater than the content of (a,b) and (x,y) is north of the inversion path of (a,b). LINKS FindStat - Combinatorial Statistic Finder, The inversion number of a standard tableau as defined by Haglund and Stevens. J. Haglund and L. Stevens, An extension of the Foata map to standard Young tableaux, SÃ©minaire Lotharingien de Combinatoire 56 (2006), Article B56c. EXAMPLE Triangle begins: 1,1, 1,1,1,1, 1,1,2,3,4,4,4,3,2,1,1, ... CROSSREFS Cf. A000085. Sequence in context: A290097 A241283 A274095 * A109870 A171502 A005102 Adjacent sequences:  A263405 A263406 A263407 * A263409 A263410 A263411 KEYWORD nonn,tabf,more AUTHOR Christian Stump, Oct 17 2015 STATUS approved

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Last modified July 31 02:33 EDT 2021. Contains 346367 sequences. (Running on oeis4.)