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%I #12 Dec 02 2023 08:12:48
%S 1,5,66,1294,33752,1100504,43060176,1965653232,102548623744,
%T 6018735869824,392498702352128,28155539333730560,2203322337542003712,
%U 186790304541786160128,17053569926181643921408,1668166923908523824576512,174057374767036007615922176
%N Expansion of e.g.f. 1/(2 - x - exp(4*x)).
%F a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 4^k * binomial(n,k) * a(n-k).
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 4^j*binomial(i, j)*v[i-j+1])); v;
%Y Cf. A006155, A367835, A367836.
%Y Cf. A285064, A343674, A355112, A367840.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Dec 02 2023
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