login
Expansion of e.g.f. 1 / (1 + log(1 - 4*x))^(3/4).
0

%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