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%I #10 Jul 18 2019 14:43:18
%S 0,1,2,8,25,73,204,565,1557,4275,11710,32022,87464,238692
%N Records in the indices of largest unsigned Stirling number of first kind: a(n) = smallest m such that c(m,n) = max_{k=0,1...,m} c(m,k).
%C Smallest m such that A065048(m-1) = c(m,n).
%C For k in the interval [a(n),a(n+1)-1], A065048(k-1) = c(k,n).
%C Ratio a(n+1)/a(n) seems to decrease and tend to exp(1) as n grows.
%e n=2 is a value for index k delivering the maximum value of c(m,k) for each fixed m in the interval [a(2),a(3)-1] = [2,7]. Then, for m in [a(3),a(4)-1] = [8,24], the maximum is given by c(m,3), and so on.
%o (PARI) { A309237(n) = my(t=prod(i=1,n-1,x+i+O(x^n)), m=n); while( polcoef(t,n-1)-polcoef(t,n-2) < 0, t*=x+m; m++); m; }
%Y Cf. A000254, A000399, A008275, A065048.
%K nonn,more
%O 0,3
%A _Max Alekseyev_, Jul 17 2019
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