A341244 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^5.

1, 0, 5, 5, 15, 25, 45, 80, 125, 210, 321, 500, 745, 1110, 1620, 2326, 3315, 4660, 6500, 8955, 12261, 16640, 22425, 29990, 39870, 52701, 69230, 90460, 117620, 152225, 196066, 251455, 321195, 408710, 518060, 654317, 823690, 1033535, 1292690, 1611970, 2004462, 2485605

Offset

5,3

Links

Table of n, a(n) for n=5..46.

Formula

G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^5.

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, 5):
seq(a(n), n=5..46);  # Alois P. Heinz, Feb 07 2021

Mathematica

nmax = 46; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^5, {x, 0, nmax}], x] // Drop[#, 5] &

Crossrefs

Cf. A000700, A001483, A022600, A327383, A338463, A341223, A341241, A341243, A341245, A341246, A341247, A341251.

Sequence in context: A100746 A185785 A185905 * A050341 A140360 A302511

Adjacent sequences: A341241 A341242 A341243 * A341245 A341246 A341247

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 07 2021

Status

approved