A341390 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^7.

1, 14, 119, 756, 3969, 18102, 74102, 278161, 972447, 3202521, 10022705, 30013914, 86475340, 240787680, 650356936, 1709167922, 4381936874, 10984062425, 26971690900, 64986689201, 153866265007, 358443604177, 822523519244, 1861072144260, 4155817046514

Offset: 7

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..10000

Crossrefs

Cf. A026007, A321952, A327385, A341384, A341385, A341386, A341387, A341388, 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, 7):
seq(a(n), n=7..31);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 31; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &