login
Expansion of Product_{k>=1} (1-q^(2*k))^2/(1-q^k)^7.
3

%I #19 Jan 10 2022 02:50:23

%S 1,7,33,126,419,1260,3509,9185,22842,54395,124784,277059,597644,

%T 1256341,2580363,5189185,10236710,19840410,37832553,71060190,

%U 131610897,240585292,434431132,775483785,1369359198,2393425484,4143057525,7106240582,12083072562,20375932566

%N Expansion of Product_{k>=1} (1-q^(2*k))^2/(1-q^k)^7.

%H Seiichi Manyama, <a href="/A350643/b350643.txt">Table of n, a(n) for n = 0..10000</a>

%H George E. Andrews and Peter Paule, <a href="https://doi.org/10.1016/j.jnt.2021.09.008">MacMahon's partition analysis XIII: Schmidt type partitions and modular forms</a>, Journal of Number Theory Available online 22 October 2021. See 7.4 p. 17.

%t m = 50; CoefficientList[Series[Product[(1 - q^(2*k))^2/(1 - q^k)^7, {k, 1, m}], {q, 0, m}], q] (* _Amiram Eldar_, Jan 09 2022 *)

%o (PARI) lista(nn) = my(q='q+O('q^nn)); Vec(prod(k=1, nn, (1-q^(2*k))^2/(1-q^k)^7));

%Y Cf. A350642, A350644.

%K nonn

%O 0,2

%A _Michel Marcus_, Jan 09 2022