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Expansion of e.g.f. 1/(1 - x + log(1 - 4*x)).
4

%I #7 Dec 02 2023 13:18:13

%S 1,5,66,1358,37592,1304536,54384080,2646247152,147186205056,

%T 9210766696320,640472632680192,48989958019395840,4087959251421060096,

%U 369547591764702870528,35976590549993421907968,3752609987262290143082496,417518648351593243448279040

%N Expansion of e.g.f. 1/(1 - x + log(1 - 4*x)).

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

%Y Cf. A052820, A367845, A367846.

%Y Cf. A367837.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 02 2023