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).

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.

Links

Table of n, a(n) for n=0..13.

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

Cf. A000254, A000399, A008275, A065048.

Sequence in context: A301819 A119854 A176855 * A037560 A138804 A212323

Adjacent sequences: A309234 A309235 A309236 * A309238 A309239 A309240

Keyword

nonn,more

Author

Max Alekseyev, Jul 17 2019

Status

approved