A341387 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^5.

1, 10, 65, 320, 1330, 4872, 16255, 50335, 146775, 407045, 1082000, 2773045, 6884650, 16620225, 39135280, 90113553, 203347645, 450516450, 981491380, 2105504205, 4452798556, 9293254605, 19158353285, 39044262235, 78719105560, 157112112293, 310599279105

Offset: 5

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..10000

Crossrefs

Cf. A026007, A321950, A327383, A341384, A341385, A341386, A341388, 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, 5):
seq(a(n), n=5..31);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 31; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^5, {x, 0, nmax}], x] // Drop[#, 5] &