A341391 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^8.

1, 16, 152, 1072, 6204, 31024, 138544, 564824, 2135902, 7580944, 25485560, 81734696, 251514840, 746123304, 2142114356, 5971477112, 16208165181, 42936937488, 111240873128, 282363615336, 703303327288, 1721329848680, 4144792701532, 9829483710112

Offset: 8

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..10000

Crossrefs

Cf. A026007, A321953, A327386, A341384, A341385, A341386, A341387, A341388, A341390.

Programs

Maple

g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(d^2/
     `if`(d::odd, 1, 2), d=numtheory[divisors](j)), j=1..n)/n)
    end:
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0,
      g(n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
    end:
a:= n-> b(n, 8):
seq(a(n), n=8..31);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 31; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^8, {x, 0, nmax}], x] // Drop[#, 8] &