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A307602 Expansion of Product_{k>=1} (1 + x^k/(1 + x)). 5
1, 1, 0, 2, -1, 4, -2, 5, -1, 4, 3, -2, 16, -21, 47, -62, 104, -131, 191, -229, 304, -344, 420, -437, 477, -413, 336, -76, -270, 927, -1792, 3155, -4904, 7402, -10519, 14694, -19761, 26226, -33847, 43162, -53776, 66178, -79679, 94562, -109606, 124618, -137468, 147061 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..500

FORMULA

G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} (-1)^(d+1) / (d*(1+x)^d)).

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 + x + x^k)/(1 + x), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 16 2019 *)

PROG

(PARI) N=66; x='x+O('x^N); Vec(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)/(d*(1+x)^d)))))

CROSSREFS

Cf. A126348, A307599, A307601.

Sequence in context: A120988 A095979 A276133 * A054269 A086450 A270439

Adjacent sequences:  A307599 A307600 A307601 * A307603 A307604 A307605

KEYWORD

sign

AUTHOR

Seiichi Manyama, Apr 18 2019

STATUS

approved

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Last modified October 15 23:54 EDT 2019. Contains 328038 sequences. (Running on oeis4.)