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E.g.f. satisfies A(x) = exp(x * (1 + x + x^2 + x^3) * A(x^4/24)).
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%I #7 Nov 29 2023 11:47:55

%S 1,1,3,13,73,386,2671,20728,175393,1553968,15520861,165541806,

%T 1869485773,22249874518,284029764383,3804116563276,53328350650081,

%U 782331158754088,12051288543702313,193028133988081918,3212490296905001781,55543932173668760221

%N E.g.f. satisfies A(x) = exp(x * (1 + x + x^2 + x^3) * A(x^4/24)).

%F a(0) = 1; a(n) = (n-1)! * Sum_{k=0..n-1} (k+1) * a(floor(k/4)) * a(n-1-k) / (24^floor(k/4) * floor(k/4)! * (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\4+1]*v[i-j]/(24^(j\4)*(j\4)!*(i-1-j)!))); v;

%Y Cf. A367754, A367755, A367757.

%Y Cf. A143568.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 29 2023