|
|
A176824
|
|
a(n) = (n+1)^n mod n^n.
|
|
6
|
|
|
0, 1, 10, 113, 1526, 24337, 450066, 9492289, 225159022, 5937424601, 172385029466, 5465884225969, 187964560069638, 6968912374274593, 277133723845128226, 11767703728247765249, 531431035966023003614, 25434534147318166381993, 1286040688679372821752042
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (n+1)^n - 2*n^n (since 2*n^n <= (n+1)^n < 3*n^n for n >= 1).
In terms of the tree function T(x) = Sum_{n >= 1} n^(n-1)*x^n/n! of A000169 the e.g.f. is T(x)*(2*x + T(x)*(T(x)-2))/(x^2*(T(x)-1)^3) = x + 10*x^2/2! + 113*x^3/3! + ... . (End)
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[Mod[(n+1)^n, n^n], {n, 30}]
|
|
PROG
|
(PARI) first(m)=vector(m, i, ((i+1)^i) % (i^i)) \\ Anders Hellström, Sep 07 2015
(SageMath) [(n+1)^n%n^n for n in range(1, 31)] # G. C. Greubel, May 23 2023
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|