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%I #20 Apr 28 2021 02:04:02
%S 1,0,4,-6,48,0,1440,-10080,120960,0,7257600,-79833600,958003200,0,
%T 348713164800,-3923023104000,41845579776000,0,12804747411456000,
%U -243290200817664000,9731608032706560000,0,2248001455555215360000,-103408066955539906560000
%N Expansion of e.g.f. log(Product_{k>0} (1 + x^k)^(1/k)).
%H Seiichi Manyama, <a href="/A338814/b338814.txt">Table of n, a(n) for n = 1..450</a>
%F a(n) = (n-1)! * A048272(n).
%t a[n_] := (n - 1)! * DivisorSum[n, (-1)^(# + 1) &]; Array[a, 25] (* _Amiram Eldar_, Apr 28 2021 *)
%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(log(prod(k=1, N, (1+x^k)^(1/k)))))
%o (PARI) {a(n) = if(n<1, 0, (n-1)!*sumdiv(n, d, (-1)^(d+1)))}
%Y Column 1 of A338813.
%Y Cf. A048272, A168243, A318249.
%K sign
%O 1,3
%A _Seiichi Manyama_, Nov 10 2020
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