A341385 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^3.

1, 6, 27, 92, 279, 762, 1952, 4725, 10968, 24551, 53346, 112932, 233755, 474288, 945384, 1854517, 3585534, 6841182, 12895246, 24035841, 44337672, 80999765, 146644746, 263249169, 468817933, 828658233, 1454315508, 2535217624, 4391290854, 7560034419, 12939963016

Offset: 3

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A026007, A027346, A321948, A327381, A341384, A341386, 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, 3):
seq(a(n), n=3..33);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 33; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^3, {x, 0, nmax}], x] // Drop[#, 3] &

Formula

a(n) ~ A027346(n). - Vaclav Kotesovec, Feb 20 2021