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%I #7 Jan 28 2020 04:50:13
%S 1,5,31,241,2231,23825,287687,3872961,57514423,934197425,16480953127,
%T 313919262625,6422468800151,140496324183185,3273117681693191,
%U 80916019512168321,2115854823935820151,58351931794643315825,1692782510862560536807,51533053881743794186081
%N L.g.f.: log(Sum_{k>=0} k! * x^k / Product_{j=1..k} (1 - j*x)).
%H Vaclav Kotesovec, <a href="/A331335/b331335.txt">Table of n, a(n) for n = 1..200</a>
%F exp(Sum_{n>=1} a(n) * x^n / n) = g.f. of A000670.
%F a(n) = n * A000670(n) - Sum_{k=1..n-1} A000670(k) * a(n-k).
%F a(n) ~ n * n! / (2 * (log(2))^(n+1)). - _Vaclav Kotesovec_, Jan 28 2020
%t nmax = 20; CoefficientList[Series[Log[Sum[k! x^k/Product[1 - j x, {j, 1, k}], {k, 0, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest
%Y Cf. A000670, A205543.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Jan 14 2020
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