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%I #14 Sep 13 2023 02:12:13
%S 1,5,45,610,11020,248870,6744350,213233400,7704814200,313199930400,
%T 14146162064400,702826758144000,38093116667766000,2236695336601458000,
%U 141433354184701746000,9582086196220281456000,692463727252196674560000
%N Expansion of e.g.f. 1 / (1 - 5 * log(1 + x)).
%F a(n) = Sum_{k=0..n} 5^k * k! * Stirling1(n,k).
%F a(0) = 1; a(n) = 5 * Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k).
%t a[n_] := Sum[5^k * k! * 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!*stirling(n, k, 1));
%Y Column k=5 of A320080.
%Y Cf. A347022, A365601, A365602, A365603.
%Y Cf. A094418, A365588.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Sep 11 2023