A341253 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^10.

1, 0, 10, 10, 55, 100, 265, 560, 1175, 2420, 4667, 9000, 16575, 30180, 53470, 93152, 159395, 268190, 444910, 727360, 1174563, 1873320, 2955010, 4611960, 7127305, 10912244, 16560430, 24924550, 37217620, 55160650, 81174270, 118651560, 172316445, 248718830, 356892660

Offset: 10

Author

Ilya Gutkovskiy, Feb 07 2021

Keywords

• nonn

Crossrefs

Cf. A000700, A001488, A022605, A327388, A338463, A341236, A341241, A341243, A341244, A341245, A341246, A341247, A341251.

Programs

Maple

g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]
      [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
    end:
b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, 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..44);  # Alois P. Heinz, Feb 07 2021

Mathematica

nmax = 44; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^10, {x, 0, nmax}], x] // Drop[#, 10] &

Formula

G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^10.