A240571 a(n) = round(n^n/n!) where round(1/2)=0.

1, 1, 2, 4, 11, 26, 65, 163, 416, 1068, 2756, 7148, 18614, 48639, 127463, 334865, 881658, 2325751, 6145597, 16263866, 43099804, 114356611, 303761260, 807692035, 2149632061, 5726042115, 15264691107, 40722913454, 108713644516, 290404350963, 776207020880

Offset: 0

Author

Vladimir Shevelev, Apr 08 2014

Keywords

• nonn
• easy

Comments

We have two versions of this sequence, this and A235496, because there is no universal agreement on how to round a number like 9/2. - N. J. A. Sloane, Dec 13 2015

According to Stirling's asymptotic formula for n!, we have lim_{n->infinity} a(n+1)/a(n) = e.

Crossrefs

Cf. A000142, A000312.

Essentially the same as A235496. - Altug Alkan, Dec 13 2015

Programs

Mathematica

Table[Round[n^n/n!], {n, 30}] (* Wesley Ivan Hurt, Apr 08 2014 *)

Formula

For n>=1, round(A000312(n)/A000142(n)).

Extensions

Name clarified by Sean A. Irvine, Jan 12 2025