A341386 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^4.

1, 8, 44, 184, 662, 2120, 6256, 17276, 45277, 113568, 274592, 643220, 1465838, 3260428, 7097338, 15153288, 31791822, 65645360, 133584864, 268213400, 531879490, 1042657088, 2022113788, 3882468712, 7384455791, 13921287616, 26026092198, 48273051172, 88868177735

Offset: 4

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..10000

Crossrefs

Cf. A026007, A027906, A321949, A327382, A341384, A341385, A341387, 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, 4):
seq(a(n), n=4..32);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 32; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^4, {x, 0, nmax}], x] // Drop[#, 4] &