A341393 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^9.

1, 18, 189, 1464, 9252, 50292, 243117, 1068939, 4344660, 16522967, 59349627, 202844007, 663615180, 2088375867, 6347592999, 18698498610, 53538715836, 149375490453, 406987481852, 1084906793142, 2834211905622, 7266665613438, 18308976116535

Offset: 9

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..10000

Crossrefs

Cf. A026007, A321954, A327387, A341384, A341385, A341386, A341387, A341388, A341390, A341391, A341394.

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, 9):
seq(a(n), n=9..31);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 31; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^9, {x, 0, nmax}], x] // Drop[#, 9] &