A341245 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^6.

1, 0, 6, 6, 21, 36, 71, 132, 222, 392, 633, 1038, 1629, 2544, 3885, 5842, 8691, 12738, 18494, 26520, 37722, 53132, 74235, 102882, 141579, 193506, 262713, 354552, 475749, 634932, 842922, 1113630, 1464450, 1917254, 2499330, 3244998, 4196966, 5408004, 6943632, 8884996

Offset

6,3

Links

Table of n, a(n) for n=6..45.

Formula

G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^6.

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, 6):
seq(a(n), n=6..45);  # Alois P. Heinz, Feb 07 2021

Mathematica

nmax = 45; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^6, {x, 0, nmax}], x] // Drop[#, 6] &

Crossrefs

Cf. A000700, A001484, A022601, A112150, A327384, A338463, A341225, A341241, A341243, A341244, A341246, A341247, A341251.

Sequence in context: A189980 A188273 A185786 * A178822 A253069 A255460

Adjacent sequences: A341242 A341243 A341244 * A341246 A341247 A341248

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 07 2021

Status

approved