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 A260984 #28 Mar 04 2025 02:47:00
%S A260984 1,2,2,2,2,2,4,4,4,4,4,6,6,8,8,8,10,10,12,12,14,16,16,18,20,22,24,26,
%T A260984 28,30,32,36,38,40,44,48,52,56,60,64,68,74,80,84,90,96,104,110,118,
%U A260984 126,134,144,152,162,172,184,196,208,220,234,248
%N A260984 Coefficients of the mock theta function chibar(q).
%D A260984 Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 17, 4th equation.
%H A260984 Vaclav Kotesovec, <a href="/A260984/b260984.txt">Table of n, a(n) for n = 0..10000</a>
%H A260984 K. Bringmann, J. Dousse, J. Lovejoy, and K. Mahlburg, <a href="https://doi.org/10.37236/5248">Overpartitions with restricted odd differences</a>, Electron. J. Combin. 22 (2015), no.3, paper 3.17.
%H A260984 K. Bringmann and J. Lovejoy, <a href="http://arxiv.org/abs/0708.0692">Dyson's rank, overpartitions, and weak Maass forms</a>, arXiv:0708.0692 [math.NT], 2007.
%H A260984 K. Bringmann and J. Lovejoy, <a href="https://doi.org/10.1093/imrn/rnm063">Dyson's rank, overpartitions, and weak Maass forms</a>, Int. Math. Res. Not. (2007), rnm063.
%F A260984 G.f.: 1 + 2*Sum_{n >= 1} q^(n*(n+1)/2)*(1+q)^2*(1+q^2)^2*...*(1+q^(n-1))^2*(1+q^n)/((1+q^3)*(1+q^6)*...*(1+q^(3*n))).
%F A260984 G.f.: -1 + 2*(1/(1-x) + x^6/((1-x)*(1-x^5)*(1-x^7)) + x^24/((1-x)*(1-x^5)*(1-x^7)*(1-x^11)*(1-x^13)) + ...). [Ramanujan] - _Michael Somos_, Sep 13 2016
%F A260984 a(n) ~ exp(Pi*sqrt(n)/3) / sqrt(3*n). - _Vaclav Kotesovec_, Jun 12 2019
%e A260984 G.f. = 1 + 2*x + 2*x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 4*x^6 + 4*x^7 + 4*x^8 + ...
%p A260984 N:= 200: # to get a(0) to a(N)
%p A260984 M:= floor((sqrt(1+8*N)-1)/2):
%p A260984 G:= 1 + 2*add(q^(n*(n+1)/2)*mul((1+q^i)^2,i=1..n-1)*(1+q^n)/mul(1+q^(3*i),i=1..n), n=1..M):
%p A260984 S:= series(G,q,N+1):
%p A260984 seq(coeff(S,q,j),j=0..N); # _Robert Israel_, Aug 06 2015
%t A260984 a[ n_] := If[ n < 1, Boole[n == 0], 2 SeriesCoefficient[ Sum[ x^(6 k^2) QPochhammer[ x^3, x^6, k] / QPochhammer[ x, x^2, 3 k + 1], {k, 0, Sqrt[n/6]}], {x, 0, n}]]; (* _Michael Somos_, Sep 13 2016 *)
%t A260984 nmax = 100; CoefficientList[Series[1 + 2*Sum[x^(k*(k+1)/2) * Product[(1 + x^j), {j, 1, k-1}]^2 * (1 + x^k) / Product[(1 + x^(3*j)), {j, 1, k}], {k, 1, Floor[Sqrt[2*nmax]]}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 12 2019 *)
%K A260984 nonn
%O A260984 0,2
%A A260984 _Jeremy Lovejoy_, Aug 06 2015