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 A277407 #13 Mar 08 2025 01:33:24
%S A277407 1,1,3,19,220,4196,120876,4915212,268194816,18903020544,1671209210880,
%T A277407 181064295924480,23589442167333120,3638090042721918720,
%U A277407 655483159341216541440,136420837710333144595200,32478481518550347674419200,8770206330674425311097651200,2666047809138871800854163456000,906320525390421790143785781657600,342508343836409428996994343026688000
%N A277407 a(n) = A277406(n)/(n+1).
%C A277407 A277406(n) equals the sum of all permutations of compositions of functions (1 + k*x) for k=1..n, evaluated at x=1.
%F A277407 a(n) = (1/(n+1)) * Sum_{k=0..n} k!*(n-k)! * Sum_{i=0..n-k+1} (-1)^(n-i+1) * Stirling2(i,n-k+1) * Stirling1(n+1,i).
%o A277407 (PARI) {a(n) = 1/(n+1) * sum(k=0, n, k!*(n-k)! * sum(i=0, n-k+1, (-1)^(n-i+1) * stirling(i, n-k+1, 2) * stirling(n+1, i, 1)))}
%o A277407 for(n=0, 20, print1(a(n), ", "))
%Y A277407 Cf. A277405, A277406.
%K A277407 nonn
%O A277407 0,3
%A A277407 _Paul D. Hanna_, Oct 16 2016