I asked George Andrews about this problem and this was part of his reply:

"Define g_1(n)=2n-1
and g_m(n)=g_m-1(n)(g_m-1+1)

Thus

g_1(n):1,3,5,7,9,11,13,15,...

g_2(n):2,12,30,56,90,132,182,...

g_3(n):6,156,930,3192,8190,17556,...

g_4(n):42,24492,865830,...

I claim that the sequence for a consists of all the values of g_m(n) for m>=1,n>=1"