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%I #17 Jun 10 2023 10:55:56
%S 1,1,5,22,105,497,2431,11976,59928,302816,1545660,7955132,41255625,
%T 215378364,1131134574,5972272636,31684600709,168824599282,
%U 903080385252,4848038120323,26110774945462,141048622038068,764026532321068,4149020129689451
%N G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 - 3*x^k)) ).
%H Seiichi Manyama, <a href="/A363546/b363546.txt">Table of n, a(n) for n = 0..1000</a>
%F A(x) = (1 - 3*x) * B(x) where B(x) is the g.f. of A363541.
%F a(n) = A363541(n) - 3*A363541(n-1) for n > 0.
%o (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, subst(A, x, x^k)*x^k/(k*(1-3*x^k)))+x*O(x^n))); Vec(A);
%Y Cf. A052855, A198518, A363545, A363580, A363581.
%Y Cf. A363541.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 09 2023
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