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 A003040 Highest degree of an irreducible representation of symmetric group S_n of degree n. (Formerly M0811) 8
 1, 1, 2, 3, 6, 16, 35, 90, 216, 768, 2310, 7700, 21450, 69498, 292864, 1153152, 4873050, 16336320, 64664600, 249420600, 1118939184, 5462865408, 28542158568, 117487079424, 547591590000, 2474843571200, 12760912164000, 57424104738000, 295284192952320 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Highest number of standard tableaux of the Ferrers diagrams of the partitions of n. Example: a(4) = 3 because to the partitions 4, 31, 22, 211, and 1111 there correspond 1, 3, 2, 3, and 1 standard tableaux, respectively. - Emeric Deutsch, Oct 02 2015 REFERENCES J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985. D. E. Littlewood, The Theory of Group Characters and Matrix Representations of Groups. 2nd ed., Oxford University Press, 1950, p. 265. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Eric M. Schmidt, Table of n, a(n) for n = 1..80 S. Comét, Improved methods to calculate the characters of the symmetric group, Math. Comp. 14 (1960) 104-117. J. McKay, The largest degrees of irreducible characters of the symmetric group. Math. Comp. 30 (1976), no. 135, 624-631. (Gives first 75 terms.) J. McKay, Page 1 of 5 pages of tables from Math. Comp. paper [reports 29th term incorrectly] Igor Pak, Greta Panova, Damir Yeliussizov, On the largest Kronecker and Littlewood-Richardson coefficients, arXiv:1804.04693 [math.CO], 2018. R. P. Stanley, Letter to N. J. A. Sloane, c. 1991 EXAMPLE a(5) = 6 because the degrees for S_5 are 1,1,4,4,5,5,6. PROG (Sage) def A003040(n) : ....res = 1 ....for P in Partitions(n) : ........res = max(res, P.dimension()) ....return res end # Eric M. Schmidt, May 07 2013 CROSSREFS A117500 gives the corresponding partitions of n. Cf. A003869, A003870, A003871, A003872, A003873, A003874, A003875, A003876, A003877. Sequence in context: A215659 A028688 A030753 * A126317 A079437 A061220 Adjacent sequences:  A003037 A003038 A003039 * A003041 A003042 A003043 KEYWORD nonn AUTHOR EXTENSIONS Entry revised and extended by N. J. A. Sloane, Apr 28 2006 a(29) corrected by Eric M. Schmidt, May 07 2013 STATUS approved

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Last modified December 17 06:45 EST 2018. Contains 318192 sequences. (Running on oeis4.)