A001099 a(n) = n^n - a(n-1), with a(1) = 1.

1, 3, 24, 232, 2893, 43763, 779780, 15997436, 371423053, 9628576947, 275683093664, 8640417354592, 294234689237661, 10817772136320355, 427076118244539020, 18019667955465012596, 809220593930871751581, 38537187481365665823843, 1939882468178947923300136

Offset: 1

Author

Ed Smiley

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A001923.

Programs

Mathematica

Abs[Table[Sum[k^k*(-1)^(k+1),{k,1,n}],{n,1,30}]] (* Alexander Adamchuk, Jun 30 2006 *)
RecurrenceTable[{a[1]==1,a[n]==n^n-a[n-1]},a,{n,20}] (* Harvey P. Dale, Jan 21 2015 *)

Python

from itertools import accumulate, count, islice
def A001099_gen(): # generator of terms
    yield from accumulate((k**k for k in count(1)),func=lambda x,y:y-x)
A001099_list = list(islice(A001099_gen(),20)) # Chai Wah Wu, Jun 17 2022

Formula

Absolute value of Sum_{k=1..n} k^k*(-1)^(k+1). a(n) = n^n - (n-1)^(n-1) + (n-2)^(n-2) - ... - (-1)^n*1^1. - Alexander Adamchuk, Jun 30 2006