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%I #9 Oct 16 2016 23:00:13
%S 1,1,3,19,220,4196,120876,4915212,268194816,18903020544,1671209210880,
%T 181064295924480,23589442167333120,3638090042721918720,
%U 655483159341216541440,136420837710333144595200,32478481518550347674419200,8770206330674425311097651200,2666047809138871800854163456000,906320525390421790143785781657600,342508343836409428996994343026688000
%N a(n) = A277406(n)/(n+1).
%C A277406(n) equals the sum of all permutations of compositions of functions (1 + k*x) for k=1..n, evaluated at x=1.
%F 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 (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 for(n=0, 20, print1(a(n), ", "))
%Y Cf. A277405, A277406.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 16 2016