A341388 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^6.

1, 12, 90, 508, 2391, 9840, 36578, 125358, 402093, 1220232, 3532836, 9821280, 26352110, 68528718, 173311971, 427486178, 1030855416, 2435255634, 5645810201, 12864839166, 28850671284, 63751119334, 138946592610, 298974483954, 635626314025

Offset: 6

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..10000

Crossrefs

Cf. A026007, A321951, A327384, A341384, A341385, A341386, A341387, A341390, A341391.

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, 6):
seq(a(n), n=6..30);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 30; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^6, {x, 0, nmax}], x] // Drop[#, 6] &