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, 650971, 1774466

Offset: 0

Author

Max Alekseyev, Jul 17 2019

Keywords

• nonn
• more

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.

Examples

			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.
		

Crossrefs

Cf. A000254, A000399, A008275, A065048.

Programs

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; }

Extensions

a(14)-a(15) from Alexander Fritsch and Johann Peters, Dec 04 2024