A274691 - OEIS

%I #37 May 19 2024 08:11:52

%S 1,1,4,7,19,33,77,135,218,392,798,1312,2381,4107,6639,11722,15869,

%T 26333,45115,69168,106213,170710,244042,384991,592859,895944,1326012,

%U 2055454,2884762,4466493,6553384,9798596,13336991,20192347,28680574,41695293,59766105,86344867

%N Number of odd entries in the character table of the symmetric group S_n.

%H Hugo Pfoertner, <a href="/A274691/b274691.txt">Table of n, a(n) for n = 0..76</a>

%H Alexander R. Miller, <a href="https://www.mat.univie.ac.at/~miller/ARMillerEvenOddNote.pdf">On parity and characters of symmetric groups</a>, preprint.

%H Alexander R. Miller, <a href="https://doi.org/10.1016/j.jcta.2018.11.001">On parity and characters of symmetric groups</a>, J. Combin. Theory Ser. A 162 (2019), 231-240. Gives terms for n <= 76.

%e For n = 2, all four character values are 1 or -1, so a(2) = 4.

%p with(combinat):

%p a:= n-> add(`if`(i[]::odd, 1, 0), i=entries(character(n))):

%p seq(a(n), n=0..15);  # _Alois P. Heinz_, Jul 10 2016

%Y Cf. A001255, A006907, A335686.

%K nonn

%O 0,3

%A _Richard Stanley_, Jul 02 2016

%E More terms from _Alois P. Heinz_, Jul 10 2016

%E Further terms from Miller (2019) added by _N. J. A. Sloane_, Jul 07 2020