I asked George Andrews about this problem and this was part of his reply:
"Define g_1(n)=2n-1$g_1(n)=2n-1$ and g_m(n)=g_m-1(n)(g_m-1+1)$g_m(n)=g_{m-1}(n)(g_{m-1}(n)+1)$
Thus
g_1(n):1,3,5,7,9,11,13,15,...$g_1(n):1,3,5,7,9,11,13,15,...$
g_2(n):2,12,30,56,90,132,182,...$g_2(n):2,12,30,56,90,132,182,...$
g_3(n):6,156,930,3192,8190,17556,...$g_3(n):6,156,930,3192,8190,17556,...$
g_4(n):42,24492,865830,...$g_4(n):42,24492,865830,...$
I claim that the sequence for a$a$ consists of all the values of g_m(n)$g_m(n)$ for m>=1,n>=1"$m\geq 1, n\geq 1$."
