cp's OEIS Frontend

A122928 Coefficients of a q-series inspired by Andrews and Ramanujan.

%I A122928 #10 Dec 11 2016 01:53:42
%S A122928 1,1,2,3,5,8,12,18,26,37,52,72,99,134,180,240,317,416,542,702,904,
%T A122928 1158,1476,1872,2364,2973,3724,4647,5778,7160,8844,10890,13370,16368,
%U A122928 19984,24336,29561,35822,43308,52242,62884,75536,90552,108342,129384,154232
%N A122928 Coefficients of a q-series inspired by Andrews and Ramanujan.
%H A122928 G. E. Andrews, <a href="http://www.mat.univie.ac.at/~slc/opapers/s25andrews.html">Three aspects of partitions</a>, Séminaire Lotharingien de Combinatoire, B25f (1990), 1 p.
%F A122928 Euler transform of period 24 sequence [ 1, 1, 1, 1, 2, 1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 1, 1, 1, 0, ...].
%F A122928 Given g.f. A(x), then B(x)=A(x)^2-A(x) satisfies 0=f(B(x), B(x^2)) where f(u, v)=(1+6*u)*v*(1+2*v)-u^2.
%F A122928 G.f.: {Sum_{k} q^(6k^2-k) }/{Sum_{k} (-1)^k q^((3k^2-k)/2) }.
%F A122928 G.f.: Product_{k>0} (1-q^(12k))(1+q^(12k-5))(1+q^(12k-7))/(1-q^k).
%F A122928 G.f.: 1+Sum_{k>0} Prod[i=1..k, (1+q^i)^2]*(1+q^k)*q^(k^2) /{(1-q)(1-q^2)...(1-q^(2k))}.
%F A122928 a(n) ~ exp(Pi*sqrt(2*n/3)) / (2^(9/4) * 3^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, Aug 31 2015
%t A122928 nmax = 100; CoefficientList[Series[Product[(1-x^(12*k))*(1+x^(12*k-5))*(1+x^(12*k-7))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 31 2015 *)
%o A122928 (PARI) {a(n)=if(n<1, n==0, polcoeff( sum(k=1, sqrtint(n), x^k^2/(1+x^k)* prod(i=1, k, (1+x^i)^2/(1-x^(2*i-1))/(1-x^(2*i)), 1+x*O(x^(n-k^2)))), n))}
%Y A122928 Cf. A098693(n)=a(n) if n>0.
%K A122928 nonn
%O A122928 0,3
%A A122928 _Michael Somos_, Sep 19 2006