%I #10 Sep 08 2022 08:46:08
%S 1,6,16,32,60,92,128,192,253,316,432,512,604,792,896,1024,1272,1410,
%T 1584,1920,2104,2236,2688,2944,3101,3732,3904,4096,4884,5080,5376,
%U 6144,6424,6776,7776,8096,8188,9492,9856,10112,11664,11704,11952,13824,14100,14360
%N Expansion of q * phi(q)^3 * psi(q^2)^4 in powers of q where phi(), psi() are Ramanujan theta functions.
%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H Vaclav Kotesovec, <a href="/A243763/b243763.txt">Table of n, a(n) for n = 1..1000</a>
%H Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F Expansion of eta(q^2)^11 * eta(q^4)^2 / eta(q)^6 in powers of q.
%F Euler transform of period 4 sequence [ 6, -5, 6, -7, ...].
%e G.f. = q + 6*q^2 + 16*q^3 + 32*q^4 + 60*q^5 + 92*q^6 + 128*q^7 + 192*q^8 + ...
%t a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q]^3 EllipticTheta[ 2, 0, q]^4 / 16, {q, 0, n}];
%t a[ n_] := SeriesCoefficient[ q QPochhammer[ q^2]^11 QPochhammer[ q^4]^2 / QPochhammer[ q]^6, {q, 0, n}];
%t nmax = 50; CoefficientList[Series[Product[(1-x^k)^7 * (1+x^(2*k))^2 * (1+x^k)^13, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 11 2016 *)
%o (PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^2 + A)^11 * eta(x^4 + A)^2 / eta(x + A)^6, n))};
%o (Magma) Basis( ModularForms( Gamma0(4), 7/2), 50) [2] ;
%K nonn
%O 1,2
%A _Michael Somos_, Jun 10 2014