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%I #18 Apr 29 2021 04:34:44
%S 1,1,2,4,8,13,22,39,65,104,160,263,413,646,975,1479,2198,3354,5017,
%T 7389,10770,15721,22668,32663,47200,67761,96389,135977,191431,268805,
%U 376211,523692,730301,1014029,1401553,1925074,2638522,3608182,4924194,6694070,9088239,12323707,16668255
%N Expansion of Product_{k>=1} (1 + x^k * (1 + k*x)).
%H Seiichi Manyama, <a href="/A336980/b336980.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) * (1 + k/d * x)^d / d).
%t m = 42; CoefficientList[Series[Product[1 + x^k*(1 + k*x), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, Apr 29 2021 *)
%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, 1+x^k*(1+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)*(1+k/d*x)^d/d))))
%Y Cf. A160571, A336975, A336976, A336977, A336978, A336979.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 09 2020
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