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A307626
Expansion of Product_{k>=1} 1/(1 - x^k/(1 + x)).
2
1, 1, 1, 1, 2, 1, 4, 0, 8, -3, 16, -12, 36, -40, 88, -117, 220, -321, 560, -860, 1447, -2284, 3772, -6032, 9861, -15864, 25798, -41627, 67527, -109132, 176826, -285985, 463089, -749189, 1212722, -1962181, 3175635, -5138421, 8315361, -13455103, 21772865
OFFSET
0,5
LINKS
FORMULA
G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} 1/(d*(1+x)^d)).
MATHEMATICA
m = 40; CoefficientList[Series[Product[1/(1 - x^k/(1 + x)), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, May 14 2021 *)
PROG
(PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, 1-x^k/(1+x)))
(PARI) N=66; x='x+O('x^N); Vec(exp(sum(k=1, N, x^k*sumdiv(k, d, 1/(d*(1+x)^d)))))
CROSSREFS
Convolution inverse A307601.
Cf. A227682.
Sequence in context: A077954 A077979 A297108 * A122161 A067164 A140505
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 19 2019
STATUS
approved