A169993 - OEIS

%I #19 Jan 07 2021 01:19:34

%S 1,1,0,1,1,1,1,1,2,2,2,2,3,3,3,4,5,5,5,6,7,7,7,8,9,10,9,11,12,12,12,

%T 13,15,15,15,16,18,17,17,18,20,19,19,20,21,21,20,21,22,22,20,22,22,21,

%U 20,21,21,20,19,19,20,18,17,17,18,16,15,15,15,13,12,12,12,11,9,10,9,8,7,7,7,6

%N Expansion of Product_{i=0..m-1} (1 + x^(2*i+1)) for m=10.

%C Product_{i=0..m-1} (1 + x^(2*i+1)) is the Poincaré polynomial for GL(m).

%C Number of self-conjugate partitions of n into at most 10 parts. Also, number of partitions of n into distinct odd parts not larger than 19. - _Álvar Ibeas_, Aug 01 2020

%D H. Weyl, The Classical Groups, Princeton, 1946, see p. 233.

%H Nathaniel Johnston, <a href="/A169993/b169993.txt">Table of n, a(n) for n = 0..100</a> (full sequence)

%F a(n) = a(100-n). - _Rick L. Shepherd_, Feb 24 2013

%Y Cf. A000700, A169987, A169988, A169989, A169990, A169991, A169992, A169994, A169995.

%K nonn,fini,full,easy

%O 0,9

%A _N. J. A. Sloane_, Aug 29 2010