A341384 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^2.

1, 4, 14, 36, 89, 200, 434, 898, 1810, 3548, 6810, 12816, 23719, 43250, 77795, 138244, 242920, 422510, 727907, 1243094, 2105493, 3538936, 5905481, 9787810, 16118588, 26383244, 42936039, 69491436, 111884015, 179239648, 285775148, 453550910, 716670609

Offset: 2

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A026007, A026011, A321947, A327380, A341385, 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, 2):
seq(a(n), n=2..34);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 34; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^2, {x, 0, nmax}], x] // Drop[#, 2] &

Formula

a(n) ~ A026011(n). - Vaclav Kotesovec, Feb 20 2021