This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A085642 #44 Jul 26 2024 11:40:09
%S A085642 0,1,1,2,3,6,8,12,17,26,35,49,66,92,121,161,211,280,360,466,596,766,
%T A085642 968,1225,1538,1935,2408,2996,3707,4588,5636,6918,8456,10329,12552,
%U A085642 15236,18431,22275,26817,32242,38661,46306,55294,65942,78464,93252,110561
%N A085642 Number of columns in the character table of the symmetric group S_n that have zero sum.
%C A085642 Conjecture: Equals the number of partitions of n with at least one part congruent to 2 mod 4. - _Vladeta Jovovic_, Jul 12 2003. This conjecture was established by _Christine Bessenrodt_ and Jorn B. Olsson (olsson(AT)math.ku.dk), Sep 13 2004.
%C A085642 Also number of partitions of n with some odd part repeated. - _Vladeta Jovovic_, Feb 05 2005
%H A085642 Vaclav Kotesovec, <a href="/A085642/b085642.txt">Table of n, a(n) for n = 1..10000</a>
%H A085642 Arvind Ayyer, Hiranya Kishore Dey, and Digjoy Paul, <a href="https://arxiv.org/abs/2406.06036">How large is the character degree sum compared to the character table sum for a finite group?</a>, arXiv preprint arXiv:2406.06036 [math.RT], 2024. See p. 6.
%H A085642 Arvind Ayyer, Hiranya Kishore Dey, and Digjoy Paul, <a href="https://www.mat.univie.ac.at/~slc/wpapers/FPSAC2024/99.pdf">On the sum of the entries in a character table</a>, Proc. 36th Conf. Formal Power Series Alg. Comb., Sem. Lotharingien Comb (2024) Vol. 91B, Art. No. 99.
%H A085642 Christine Bessenrodt and Jorn Olsson, <a href="/A085642/a085642.pdf">On the sequence A085642</a>
%H A085642 Dominique Gouyou-Beauchamps and Philippe Nadeau, <a href="http://igm.univ-mlv.fr/~fpsac/FPSAC07/SITE07/PDF-Proceedings/Posters/13.pdf">Signed Enumeration of Ribbon Tableaux with Local Rules and Generalizations of the Schensted Correspondence</a>, in Formal Power Series and Algebraic Combinatorics, Nankai University, Tianjin, China, 2007.
%H A085642 Dominique Gouyou-Beauchamps and Philippe Nadeau, <a href="https://hal.archives-ouvertes.fr/hal-02065198">Signed enumeration of ribbon tableaux: an approach through growth diagrams</a>, Journal of Algebraic Combinatorics, 2011; DOI 10.1007/s10801-011-0324-2.
%F A085642 a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*n*sqrt(3)). - _Vaclav Kotesovec_, Jul 11 2018
%t A085642 Rest[PartitionsP[Range[0,47]] - CoefficientList[Series[Product[(1+x^(2 k - 1))/(1 - x^(2 k)), {k,48}], {x,0,47}], x]] (* _Wouter Meeussen_, Dec 20 2017 *)
%Y A085642 Cf. A006950, A082733.
%K A085642 nonn
%O A085642 1,4
%A A085642 Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 11 2003
%E A085642 Corrected and extended by _Vladeta Jovovic_, Jul 12 2003
%E A085642 More terms from _David Wasserman_, Feb 08 2005