%I A003040 M0811
%S A003040 1,1,2,3,6,16,35,90,216,768,2310,7700,21450,69498,292864,1153152,
%T A003040 4873050,16336320,64664600,249420600,1118939184,5462865408,28542158568,
%U A003040 117487079424,547591590000,2474843571200,12760912164000,57424104738000,
               295284192942320
%N A003040 Highest degree of an irreducible representation of symmetric group S_n 
               of degree n.
%D A003040 S. Come't, Improved methods to calculate the characters of the symmetric 
               group, Math. Comp. 14 (1960) 104-117.
%D A003040 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 A003040 D. E. Littlewood, The Theory of Group Characters and Matrix Representations 
               of Groups. 2nd ed., Oxford University Press, 1950, p. 265.
%D A003040 J. McKay, The largest degrees of irreducible characters of the symmetric 
               group. Math. Comp. 30 (1976), no. 135, 624-631. (Gives first 75 terms.)
%D A003040 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A003040 J. McKay, <a href="a003040a.jpg">Page 1 of 5 pages of tables from Math. 
               Comp. paper</a>
%H A003040 J. McKay, <a href="a003040b.jpg">Page 2 of 5 pages of tables from Math. 
               Comp. paper</a>
%H A003040 J. McKay, <a href="a003040c.jpg">Page 3 of 5 pages of tables from Math. 
               Comp. paper</a>
%H A003040 J. McKay, <a href="a003040d.jpg">Page 4 of 5 pages of tables from Math. 
               Comp. paper</a>
%H A003040 J. McKay, <a href="a003040e.jpg">Page 5 of 5 pages of tables from Math. 
               Comp. paper</a>
%e A003040 a(5) = 6 because the degrees for S_5 are 1,1,4,4,5,5,6.
%Y A003040 A117500 gives the corresponding partitions of n.
%Y A003040 Cf. A003869, A003870, A003871, A003872, A003873, A003874, A003875, A003876, 
               A003877.
%Y A003040 Sequence in context: A109162 A028688 A030753 this_sequence A126317 A079437 
               A061220
%Y A003040 Adjacent sequences: A003037 A003038 A003039 this_sequence A003041 A003042 
               A003043
%K A003040 nonn
%O A003040 1,3
%A A003040 N. J. A. Sloane (njas(AT)research.att.com), R. P. Stanley
%E A003040 Entry revised and extended by N. J. A. Sloane (njas(AT)research.att.com), 
               Apr 28 2006