|
%I #22 Nov 11 2023 05:09:21
%S 1,5,55,910,20080,553870,18333050,707959800,31244562600,1551289408800,
%T 85579293493200,5193226343508000,343790892166398000,
%U 24655487205067386000,1904221630155352038000,157574022827034258192000,13908505761692419540320000
%N Expansion of e.g.f. 1 / (1 + 5 * log(1-x)).
%H Seiichi Manyama, <a href="/A365588/b365588.txt">Table of n, a(n) for n = 0..350</a>
%F a(n) = Sum_{k=0..n} 5^k * k! * |Stirling1(n,k)|.
%F a(0) = 1; a(n) = 5 * Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).
%F a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / (5 * exp(4*n/5) * (exp(1/5) - 1)^(n+1)). - _Vaclav Kotesovec_, Nov 11 2023
%t a[n_] := Sum[5^k * k! * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 17, 0] (* _Amiram Eldar_, Sep 13 2023 *)
%o (PARI) a(n) = sum(k=0, n, 5^k*k!*abs(stirling(n, k, 1)));
%Y Column k=5 of A320079.
%Y Cf. A346987, A365585, A365586, A365587.
%Y Cf. A094418.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Sep 10 2023
|
