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A309237
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).
4
0, 1, 2, 8, 25, 73, 204, 565, 1557, 4275, 11710, 32022, 87464, 238692
OFFSET
0,3
COMMENTS
Smallest m such that A065048(m-1) = c(m,n).
For k in the interval [a(n),a(n+1)-1], A065048(k-1) = c(k,n).
Ratio a(n+1)/a(n) seems to decrease and tend to exp(1) as n grows.
EXAMPLE
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.
PROG
(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; }
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Max Alekseyev, Jul 17 2019
STATUS
approved