%I #8 Nov 18 2023 08:36:03
%S 1,3,33,579,13857,419427,15344769,658225635,32388324801,1798082759235,
%T 111173908726881,7575821838083331,564099365435411169,
%U 45567223702943324067,3968829692958916703169,370764641464637535547299,36980399763333881818665345
%N Expansion of e.g.f. 1 / (1 + log(1 - 4*x))^(3/4).
%F a(n) = Sum_{k=0..n} 4^(n-k) * (Product_{j=0..k-1} (4*j+3)) * |Stirling1(n,k)|.
%F a(0) = 1; a(n) = Sum_{k=1..n} 4^k * (1 - 1/4 * k/n) * (k-1)! * binomial(n,k) * a(n-k).
%o (PARI) a(n) = sum(k=0, n, 4^(n-k)*prod(j=0, k-1, 4*j+3)*abs(stirling(n, k, 1)));
%Y Cf. A367429.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Nov 18 2023