A235496 a(n) = round(n^n/n!) where round(1/2)=1.

1, 1, 2, 5, 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

Vincenzo Librandi, Jan 15 2014

Keywords

• nonn
• easy

Comments

We have two versions of this sequence, this and A240571, because there is no universal agreement on how to round a number like 9/2. - N. J. A. Sloane, Dec 13 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000142, A000312, A055775, A073225.

See A240571 for another version.

Programs

Magma

[Round(n^n/Factorial(n)): n in [1..40]];

Maple

a:= n-> round(n^n/n!):
seq(a(n), n=0..32);  # Alois P. Heinz, Dec 13 2015

Mathematica

Table[Floor[n^n/n! + 1/2], {n, 40}]

PARI

s=[]; for(n=1, 30, s=concat(s, round(n^n/n!))); s \\ Colin Barker, Jan 19 2014

Formula

a(n) = Round(A000312(n)/A000142(n)).

Extensions

Name clarified by Sean A. Irvine, Jan 12 2025