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 A082733 #56 Jun 11 2025 17:19:35
%S A082733 1,2,5,13,31,89,259,842,2810,10020,37266,145373,586071,2453927,
%T A082733 10590180,47159351,215706629,1013916313,4882544468,24087770591,
%U A082733 121481296510,626169893024,3293432146879,17670096206819,96589760733604,537731396393480,3045955783377644
%N A082733 Sum of all entries in character table of the symmetric group S_n.
%H A082733 Ludovic Schwob, <a href="/A082733/b082733.txt">Table of n, a(n) for n = 1..200</a>
%H A082733 Ron M. Adin, Alexander Postnikov, and Yuval Roichman! <a href="https://doi.org/10.1016/j.jalgebra.2008.03.030">Combinatorial Gelfand models</a>, J. Algebra, 320(3):1311-1325, 2008.
%H A082733 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. 5.
%H A082733 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>, Proceedings of the 36th Conference on Formal Power Series and Algebraic Combinatorics (Bochum), Séminaire Lotharingien de Combinatoire 91B (2024), Article #99, 12 pp.
%H A082733 Joseph Ben Geloun and Sanjaye Ramgoolam, <a href="http://arxiv.org/abs/1307.6490">Counting Tensor Model Observables and Branched Covers of the 2-Sphere</a>, arXiv preprint arXiv:1307.6490 [hep-th], 2013.
%H A082733 Ludovic Schwob, <a href="https://arxiv.org/abs/2506.04007">On the enumeration of double cosets and self-inverse double cosets</a>, arXiv:2506.04007 [math.CO], 2025. See p. 5.
%F A082733 Let D(x) = Sum_{n>=0} (2n-1)!!*x^n = 1/(1 - x/(1 - 2x/(1 - 3x/...))) and R_r(x) = Sum_{n>=0} o_r(n)*x^n = 1/(1 - x - r*x^2/(1 - x - 2*r*x^2/(1 - x - 3*r*x^2/...))), where o_r(n) = Sum_{k=0..n/2} binomial(n, 2k)*(2k-1)!!*r^k. Then the generating function of this sequence is Sum_{n>=0} a(n)*x^n = Product_{i >= 1} (D(2ix^{4i}) * R_{2i-1}(x^{2i-1}). - _Arvind Ayyer_, Jun 11 2024
%e A082733 a(3) = 5 because the character table of S_3 is / 1 1 1 / 2 0 -1 / 1 -1 1 /.
%t A082733 a[n_] := FiniteGroupData[{"SymmetricGroup", n}, "CharacterTable"] // Flatten // Total;
%t A082733 Table[an = a[n]; Print[n, " ", an]; an, {n, 1, 10}] (* _Jean-François Alcover_, Nov 03 2018 *)
%o A082733 (GAP) A082733 := n -> Sum(Sum(Irr(CharacterTable("Symmetric", n)))); # _Eric M. Schmidt_, Jul 03 2012
%Y A082733 Cf. A086808, A085624, A085646.
%K A082733 nonn
%O A082733 1,2
%A A082733 _Vladeta Jovovic_, May 20 2003
%E A082733 More terms from _Eric M. Schmidt_, Jul 03 2012