A090205 a(n) = n^n * (n+1)^(n+1).
1, 4, 108, 6912, 800000, 145800000, 38423222208, 13816758796288, 6499837226778624, 3874204890000000000, 2853116706110000000000, 2543867514227405321404416, 2700464873652770753916960768, 3365550251744726983606907650048, 4865879898782263021500000000000000
Offset: 0
Examples
a(4) = 4^4 * 5^5 = 256 * 3125 = 800000.
Links
- H. J. Brothers and J. A. Knox, New closed-form approximations to the logarithmic constant e, Math. Intelligencer, 20 (1998), 25-29.
Programs
-
Mathematica
Table[n^n (n+1)^(n+1),{n,20}] (* Harvey P. Dale, May 29 2016 *) Denominator[Table[(n + 2)^(n + 2)/(n + 1)^(n + 1) - (n + 1)^(n + 1)/n^n, {n, 20}]] (* Harlan J. Brothers, Aug 25 2023 *) Join[{1},Times@@@Partition[Table[n^n,{n,20}],2,1]] (* Harvey P. Dale, Feb 04 2024 *) -
Maxima
A090205[n]:=n^n*(n+1)^(n+1)$ makelist(A090205[n],n,1,30); /* Martin Ettl, Oct 29 2012 */
Formula
a(n) ~ e^(1 + 1/(2*n)) * n^(2*n+1). - Harlan J. Brothers, Aug 25 2023
Extensions
More terms from Harlan J. Brothers, Aug 25 2023
Comments