This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383232 #8 Apr 20 2025 08:57:09
%S A383232 0,1,9,122,2242,52180,1471692,48790608,1859539344,80109265824,
%T A383232 3849497255520,204138860091264,11842095171021696,745962168915065088,
%U A383232 50708105952635996928,3699802551156676392960,288399758863879774476288,23919432333548949807869952,2103184085769044913951461376
%N A383232 Expansion of e.g.f. f(x)^2 * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).
%F A383232 a(n) = Sum_{k=1..n} k * 2^(k-1) * 5^(n-k) * |Stirling1(n,k)|.
%F A383232 a(n) = 5^(n-1) * n! * Sum_{k=0..n-1} (-1)^k * binomial(-2/5,k)/(n-k).
%F A383232 a(n) = (10*n-11) * a(n-1) - (5*n-8)^2 * a(n-2) for n > 1.
%o A383232 (PARI) a(n) = sum(k=1, n, k*2^(k-1)*5^(n-k)*abs(stirling(n, k, 1)));
%Y A383232 Cf. A383231, A383233, A383234.
%K A383232 nonn
%O A383232 0,3
%A A383232 _Seiichi Manyama_, Apr 20 2025