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 A079499 #36 Jan 19 2022 20:16:22
%S A079499 0,1,0,1,2,1,2,1,4,4,4,4,6,7,6,10,12,13,12,16,18,22,22,25,32,36,36,42,
%T A079499 50,53,58,64,76,83,88,99,116,123,132,147,168,181,194,215,240,262,280,
%U A079499 306,346,375,396,437,482,521,558,610,670,724,772,840,922,993,1056,1151,1256,1348
%N A079499 Total number of parts in all partitions of n into distinct odd parts.
%C A079499 Also sum of the sizes of the Durfee squares of all self-conjugate partitions of n. Example: a(13)=7 because there are three self-conjugate partitions of 13, namely [7,1,1,1,1,1,1], [5,3,3,1,1] and [4,4,3,2], having Durfee squares of sizes 1,3 and 3, respectively. a(n) = Sum_{k=1..floor(sqrt(n))} k*A116422(n,k). - _Emeric Deutsch_, Feb 14 2006
%D A079499 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976 (pp. 27-28).
%D A079499 G. E. Andrews and K. Eriksson, Integer Partitions, Cambridge Univ. Press, 2004 (pp. 75-78).
%H A079499 Vaclav Kotesovec, <a href="/A079499/b079499.txt">Table of n, a(n) for n = 0..20000</a> (terms 0..1000 from T. D. Noe)
%H A079499 Arnold Knopfmacher and Neville Robbins, <a href="http://www.plouffe.fr/OEIS/citations/robbinspart.pdf">Identities for the total number of parts in partitions of integers</a>, Util. Math. 67 (2005), 9-18.
%F A079499 G.f.: (Sum_{k>=1} x^(2*k-1)/(1 + x^(2*k-1))) * Product_{m>=1} (1 + x^(2m-1)).
%F A079499 G.f.: Sum_{k>=1} k*x^(k^2)/Product_{j=1..k} (1 - x^(2*j)). - _Vladeta Jovovic_, Aug 06 2004
%F A079499 a(n) ~ 3^(1/4) * log(2) * exp(Pi*sqrt(n/6)) / (Pi * 2^(5/4) * n^(1/4)). - _Vaclav Kotesovec_, May 20 2018
%e A079499 a(13)=7 because the partitions of 13 into distinct odd parts are [13], [9,3,1] and [7,5,1] and we have 1+3+3=7 parts.
%p A079499 g:=sum(k*x^(k^2)/product(1-x^(2*i),i =1..k),k=1..20):gser:=series(g,x=0,52): seq(coeff(gser,x,n),n=0..50); # _Emeric Deutsch_, Feb 14 2006
%t A079499 max = 100; s = Sum[ k*x^(k^2) / Product[1-x^(2*j), {j, 1, k}], {k, 1, Sqrt[max] // Ceiling}]; CoefficientList[ Series[s, {x, 0, max}], x] (* _Jean-François Alcover_, Feb 19 2015, after _Vladeta Jovovic_ *)
%o A079499 (PARI)
%o A079499 N=66; S=2+sqrtint(N); x='x+O('x^N);
%o A079499 gf=sum(n=0, S, n*x^(n^2)/prod(k=1,n, 1-x^(2*k)) );
%o A079499 concat( [0], Vec(gf) )
%o A079499 \\ _Joerg Arndt_, Feb 18 2014
%Y A079499 Cf. A015723, A000700, A067619, A006128.
%Y A079499 Cf. A032021.
%Y A079499 Cf. A116422.
%K A079499 nonn
%O A079499 0,5
%A A079499 _Arnold Knopfmacher_, Jan 21 2003