A341394 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^10.

1, 20, 230, 1940, 13285, 77944, 405250, 1910330, 8300380, 33655860, 128574734, 466317760, 1615509765, 5373215450, 17230062315, 53457917856, 160963157005, 471587847690, 1347417640405, 3761860656610, 10280578499844, 27543107112940, 72440412567485

Offset: 10

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..10000

Crossrefs

Cf. A026007, A321955, A327388, A341384, A341385, A341386, A341387, A341388, A341390, A341391, A341393.

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, 10):
seq(a(n), n=10..32);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 32; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^10, {x, 0, nmax}], x] // Drop[#, 10] &