A341244 - OEIS

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

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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)),