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 A067619 #22 Dec 23 2019 23:31:58 %S A067619 0,1,0,2,2,3,3,4,7,8,9,10,15,16,18,23,30,32,35,42,51,59,63,73,89,100, %T A067619 106,125,145,160,174,198,229,255,274,310,355,388,420,472,534,582,631, %U A067619 701,784,859,928,1021,1144,1243,1338,1475,1630,1767,1909,2089,2299 %N A067619 Total number of parts in all self-conjugate partitions of n. Also, sum of largest parts of all self-conjugate partitions of n. %H A067619 T. D. Noe, <a href="/A067619/b067619.txt">Table of n, a(n) for n = 0..1000</a> %H A067619 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 A067619 G.f.: A(q) = Sum_{n >= 1} n*q^(2*n-1)*(1+q)*(1+q^3)*...*(1+q^(2*n-3)). %F A067619 From _Peter Bala_, Aug 20 2017: (Start) %F A067619 Let F(q) = Product_{i >= 1} (1 + q^(2*i-1)). Then A(q) = Sum_{n >= 0} ( F(q) - Product_{i = 1..n} (1 + q^(2*i-1)) ). %F A067619 It follows that the above sum A(q) satisfies -A(q-1) = 1 + q + 3*q^2 + 12*q^3 + 61*q^4 + ..., the g.f. for A158691, row-Fishburn matrices of size n. (End) %t A067619 CoefficientList[Series[Sum[n*q^(2n-1)*Product[1+q^k, {k, 1, 2n-3, 2}], {n, 1, 30}], {q, 0, 60}], q] %Y A067619 Cf. A000700, A000701, A006128, A015723, A046682, A079499, A158691. %K A067619 easy,nonn %O A067619 0,4 %A A067619 _Naohiro Nomoto_, Feb 01 2002 %E A067619 Edited by _Dean Hickerson_, Feb 11 2002