A068792 a(n) = (n-1)*n^(n-2) + Sum_{i=1..n} (n-i)*(n^(n-i-1) + n^(n+i-3)).

1, 16, 441, 24336, 2418025, 384473664, 89755965649, 28953439105600, 12345678987654321, 6727499948806851600, 4562491230669011577289, 3769449794266138309731600, 3727710895159027432980276121, 4348096581244536814777202995456, 5907679981266292758213173560296225

Offset: 2

Author

Reinhard Zumkeller, Mar 04 2002

Keywords

• nonn

Comments

a(n) is a palindrome in base n representation for all n.

Examples

			a(8) = 89755965649 = (1234567654321)OCT;
a(10) = 12345678987654321 = A057139(9);
a(16) = 5907679981266292758213173560296225 = (123456789ABC...987654321)HEX.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 2..215

Crossrefs

Cf. A023811, A060072, A062813, A068793.

Programs

Magma

[((n^(n-1) -1)/(n-1))^2: n in [2..30]]; // G. C. Greubel, Aug 16 2022

Mathematica

Table[((n^(n-1) -1)/(n-1))^2, {n,2,30}] (* G. C. Greubel, Aug 16 2022 *)

Python

def A068792(n): return ((n**(n-1)-1)//(n-1))**2 # Chai Wah Wu, Mar 18 2024

SageMath

[((n^(n-1) -1)/(n-1))^2 for n in (2..30)] # G. C. Greubel, Aug 16 2022

Formula

a(n) = ( (n^(n-1) - 1)/(n-1) )^2.

a(n) = ((A023811(n) - n + 1)/n)*n^(n-1) + A062813(n)/n.

a(n) = A060072(n)^2.

Extensions

More terms from G. C. Greubel, Aug 16 2022