%I #12 Sep 13 2023 02:10:19

%S 1,3,27,390,7770,197520,6108720,222585360,9337369920,443180705520,

%T 23478556469040,1373311758143520,87902002849402080,

%U 6111187336982764800,458573390187299798400,36939974397639066086400,3179423992959428231894400,291190738388834303603395200

%N Expansion of e.g.f. 1 / (1 + 5 * log(1-x))^(3/5).

%F a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (5*j+3)) * |Stirling1(n,k)|.

%F a(0) = 1; a(n) = Sum_{k=1..n} (5 - 2*k/n) * (k-1)! * binomial(n,k) * a(n-k).

%t a[n_] := Sum[Product[5*j + 3, {j, 0, k - 1}] * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 18, 0] (* _Amiram Eldar_, Sep 13 2023 *)

%o (PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+3)*abs(stirling(n, k, 1)));

%Y Cf. A346987, A365585, A365587, A365588.

%Y Cf. A365569.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 10 2023