A214698 a(n) = (n^n - n^2)/2.

0, 0, 9, 120, 1550, 23310, 411747, 8388576, 193710204, 4999999950, 142655835245, 4458050224056, 151437553296042, 5556003412778910, 218946945190429575, 9223372036854775680, 413620130943168381944, 19673204037648268787550, 989209827830156794561809, 52428799999999999999999800

Offset: 1

Author

Alex Ratushnyak, Jul 26 2012

Keywords

• nonn
• easy

Examples

			a(3) = (27 - 9)/2 = 9.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..386

Crossrefs

Cf. A124797 is essentially equal to (n^n-n)/2.

Cf. A000217, A117694, A214647.

Programs

Magma

[(n^n -n^2)/2: n in [1..30]]; // G. C. Greubel, Jan 08 2024

Maple

A214698:= proc(n)
    (n^n-n^2)/2 ;
end proc: # R. J. Mathar, Aug 07 2012

Mathematica

Table[(n^n-n^2)/2,{n,30}] (* Harvey P. Dale, Dec 25 2022 *)

Python

for n in range(1, 22):
    print((n**n - n*n)//2)

SageMath

[(n^n -n^2)/2 for n in range(1,31)] # G. C. Greubel, Jan 08 2024

Formula

a(n) = A214647(n) - n^2 = A117694(n) - A000217(n).

E.g.f.: (-1/2)*(lambertW(-x)/(1 + lambertW(-x)) + x*(x+1)*exp(x)). - G. C. Greubel, Jan 08 2024