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%I #10 Nov 18 2023 08:27:40
%S 1,3,9,75,465,7827,54489,1985883,5684385,1038408483,-8440926039,
%T 1026884514411,-24803157926799,1735078791616947,-69866656826056839,
%U 4467425545047012219,-239734355869361550015,15985164846462976491075,-1031464442408734822175415
%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 * (1/4 * k/n - 1) * (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)*stirling(n, k, 1));
%Y Cf. A352073, A365600.
%K sign
%O 0,2
%A _Seiichi Manyama_, Nov 18 2023
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