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 A061343 Number of standard shifted tableaux with n entries. 3
 1, 1, 2, 3, 6, 12, 27, 63, 154, 398, 1055, 2970, 8503, 25651, 78483, 250487, 811802, 2723130, 9295483, 32653552, 116866283, 428464743, 1600474365, 6102119282, 23690388631, 93631999867, 376561553417, 1538997717423, 6395852269479, 26978392034357, 115628083386280, 502520979828775 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Number of ballot sequences (see A000085) where the number of occurrences of k in any prefix is strictly greater than the number of occurrences of k+1. - Joerg Arndt, May 21 2016 REFERENCES D. E. Knuth, The art of computer programming, Vol. 3 (Sorting and searching), page 71, Section 5.1.4, Exercise 21 (page 67 in the second edition). LINKS Joerg Arndt, Table of n, a(n) for n = 1..101 Joerg Arndt, Pari/GP script to compute terms. R. Srinivasan, On a theorem of Thrall in combinatorial analysis, The American Mathematical Monthly, 70(1), 1963, pp. 41-44. R. M. Thrall, A combinatorial problem, Michigan Math. J. 1, (1952), 81-88. FORMULA a(n) is the sum over all partitions into distinct parts of Thrall's formula (4) on page 83, see the Pari script arndt-A061343.gp. [Joerg Arndt, May 09 2013] EXAMPLE From Joerg Arndt, May 21 2016: (Start) The a(7) = 27 tableaux correspond to the following ballot sequences (dots denote zeros). ##:     ballot sequence          partition 01:    [ . . . . . . . ]       [ 7 . . . . . . ] 02:    [ . . . . . . 1 ]       [ 6 1 . . . . . ] 03:    [ . . . . . 1 . ]       [ 6 1 . . . . . ] 04:    [ . . . . . 1 1 ]       [ 5 2 . . . . . ] 05:    [ . . . . 1 . . ]       [ 6 1 . . . . . ] 06:    [ . . . . 1 . 1 ]       [ 5 2 . . . . . ] 07:    [ . . . . 1 1 . ]       [ 5 2 . . . . . ] 08:    [ . . . . 1 1 1 ]       [ 4 3 . . . . . ] 09:    [ . . . . 1 1 2 ]       [ 4 2 1 . . . . ] 10:    [ . . . 1 . . . ]       [ 6 1 . . . . . ] 11:    [ . . . 1 . . 1 ]       [ 5 2 . . . . . ] 12:    [ . . . 1 . 1 . ]       [ 5 2 . . . . . ] 13:    [ . . . 1 . 1 1 ]       [ 4 3 . . . . . ] 14:    [ . . . 1 . 1 2 ]       [ 4 2 1 . . . . ] 15:    [ . . . 1 1 . . ]       [ 5 2 . . . . . ] 16:    [ . . . 1 1 . 1 ]       [ 4 3 . . . . . ] 17:    [ . . . 1 1 . 2 ]       [ 4 2 1 . . . . ] 18:    [ . . . 1 1 2 . ]       [ 4 2 1 . . . . ] 19:    [ . . 1 . . . . ]       [ 6 1 . . . . . ] 20:    [ . . 1 . . . 1 ]       [ 5 2 . . . . . ] 21:    [ . . 1 . . 1 . ]       [ 5 2 . . . . . ] 22:    [ . . 1 . . 1 1 ]       [ 4 3 . . . . . ] 23:    [ . . 1 . . 1 2 ]       [ 4 2 1 . . . . ] 24:    [ . . 1 . 1 . . ]       [ 5 2 . . . . . ] 25:    [ . . 1 . 1 . 1 ]       [ 4 3 . . . . . ] 26:    [ . . 1 . 1 . 2 ]       [ 4 2 1 . . . . ] 27:    [ . . 1 . 1 2 . ]       [ 4 2 1 . . . . ] (End) CROSSREFS Cf. A000085, A003121 (strict ballot sequences with partition [j, j-1, ..., 3, 2, 1]). Sequence in context: A019525 A108915 A082395 * A057649 A104872 A006082 Adjacent sequences:  A061340 A061341 A061342 * A061344 A061345 A061346 KEYWORD nonn,nice AUTHOR V. Reiner and D. White (reiner(AT)math.umn.edu), Jun 07 2001 EXTENSIONS More terms from Joerg Arndt, May 08 2013 STATUS approved

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Last modified October 16 11:32 EDT 2019. Contains 328056 sequences. (Running on oeis4.)