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E.g.f. satisfies A(x) = exp(x * (1 + x + x^2) * A(x^3)).
3

%I #12 Nov 29 2023 11:40:37

%S 1,1,3,13,73,501,4051,40153,434673,5231593,71641891,1051099941,

%T 16673401273,289579557853,5336892479283,104679769486321,

%U 2199654959898721,48682858073000913,1135029742772833603,27968526823231736893,721419709386600131241

%N E.g.f. satisfies A(x) = exp(x * (1 + x + x^2) * A(x^3)).

%F a(0) = 1; a(n) = (n-1)! * Sum_{k=0..n-1} (k+1) * a(floor(k/3)) * a(n-1-k) / (floor(k/3)! * (n-1-k)!).

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=0, i-1, (j+1)*v[j\3+1]*v[i-j]/((j\3)!*(i-1-j)!))); v;

%Y Cf. A367747, A367749, A367751.

%Y Cf. A367652, A367719.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 29 2023