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Expansion of Product_{k>=1} (1 + x^k * (k + x)).
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%I #20 May 01 2021 17:43:36

%S 1,1,3,6,11,21,37,69,108,192,312,522,827,1297,2032,3240,4982,7569,

%T 11508,17107,25696,38340,57080,83298,121373,175653,253455,364307,

%U 523650,747487,1063375,1498471,2106317,2955154,4124071,5750547,8000706,11104596,15324290,21093106

%N Expansion of Product_{k>=1} (1 + x^k * (k + x)).

%H Seiichi Manyama, <a href="/A336979/b336979.txt">Table of n, a(n) for n = 0..1000</a>

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

%t m = 39; CoefficientList[Series[Product[1 + x^k*(k + x), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, May 01 2021 *)

%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, 1+x^k*(k+x)))

%o (PARI) N=66; x='x+O('x^N); Vec(exp(sum(k=1, N, x^k*sumdiv(k, d, (-1)^(d+1)*(k/d+x)^d/d))))

%Y Cf. A022629, A160571, A336975, A336976, A336977, A336978, A336980.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 09 2020