%I #9 Nov 20 2023 11:54:54
%S 1,0,3,18,195,2730,47745,1001742,24523401,686190258,21601161015,
%T 755533274826,29066119327179,1219715093642838,55441103383640793,
%U 2713468284508412430,142269924567096468177,7955396173559375208426,472576083221524737100311
%N Expansion of e.g.f. 1/(4 - 3*exp(x))^(x/2).
%F a(0) = 1; a(n) = (1/2) * Sum_{k=1..n} A367490(k) * binomial(n-1,k-1) * a(n-k).
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*sum(k=1, j-1, 3^k*(k-1)!*stirling(j-1, k, 2))*binomial(i-1, j-1)*v[i-j+1])/2); v;
%Y Cf. A354412, A367485.
%Y Cf. A367490.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 19 2023
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