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%I #15 Aug 17 2021 10:11:06
%S 1,-1,-1,-7,25,-41,631,881,98897,-609265,3798991,-41799671,914146729,
%T -15008576857,16469525255,-5181463756351,79515495724321,
%U -1220435382764129,12608713897126687,-449855614172366695,10437031873016276921,-231918657853281955081
%N E.g.f.: exp(-Sum_{n>=1} A001227(n) * x^n).
%H Seiichi Manyama, <a href="/A294459/b294459.txt">Table of n, a(n) for n = 0..446</a>
%F a(0) = 1 and a(n) = (-1) * (n-1)! * Sum_{k=1..n} k*A001227(k)*a(n-k)/(n-k)! for n > 0.
%F E.g.f.: Product_{k>=1} 1 / (1 + x^k)^f(k), where f(k) = (1/k) * Sum_{j=1..k} gcd(k,j). - _Ilya Gutkovskiy_, Aug 17 2021
%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(-sum(k=1, N, sumdiv(k, d, d%2)*x^k))))
%Y E.g.f.: exp(-Sum_{n>=1} (Sum_{d|n and d is odd} d^k) * x^n): this sequence (k=0), A294460 (k=1), A294461 (k=2).
%Y Cf. A018804.
%K sign
%O 0,4
%A _Seiichi Manyama_, Oct 31 2017
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