%I #29 Nov 18 2023 08:27:30

%S 1,1,1,17,1,1889,-12415,631665,-11224575,461864385,-13754112255,

%T 596055636945,-24148300842495,1181210529292065,-59009709972278655,

%U 3297137505670374705,-193318225258785780735,12263541239089421903745,-820804950905249837195775

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

%F a(n) = Sum_{k=0..n} 4^(n-k) * (Product_{j=0..k-1} (4*j+1)) * Stirling1(n,k).

%F a(0) = 1; a(n) = Sum_{k=1..n} (-4)^k * (3/4 * k/n - 1) * (k-1)! * binomial(n,k) * a(n-k). - _Seiichi Manyama_, Nov 18 2023

%t m = 18; Range[0, m]! * CoefficientList[Series[(1 - Log[1 + 4*x])^(-1/4), {x, 0, m}], x] (* _Amiram Eldar_, Mar 05 2022 *)

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-log(1+4*x))^(1/4)))

%o (PARI) a(n) = sum(k=0, n, 4^(n-k)*prod(j=0, k-1, 4*j+1)*stirling(n, k, 1));

%Y Cf. A006252, A097397, A352070.

%Y Cf. A007696, A008545, A352119.

%K sign

%O 0,4

%A _Seiichi Manyama_, Mar 05 2022