A326501 a(n) = Sum_{k=0..n} (-k)^k.

1, 0, 4, -23, 233, -2892, 43764, -779779, 15997437, -371423052, 9628576948, -275683093663, 8640417354593, -294234689237660, 10817772136320356, -427076118244539019, 18019667955465012597, -809220593930871751580, 38537187481365665823844

Offset: 0

Author

Seiichi Manyama, Sep 12 2019

Keywords

• sign
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..386

Crossrefs

Cf. A001099, A062970, A177885.

Programs

Maple

a:= proc(n) option remember; `if`(n<0, 0, (-n)^n+a(n-1)) end:
seq(a(n), n=0..23);  # Alois P. Heinz, Sep 12 2019

Mathematica

RecurrenceTable[{a[0] == 1, a[n] == a[n-1] + (-n)^n}, a, {n, 0, 23}] (* Jean-François Alcover, Nov 27 2020 *)

PARI

{a(n) = sum(k=0, n, (-k)^k)}

Python

from itertools import accumulate, count, islice
def A326501_gen(): # generator of terms
    yield from accumulate((-k)**k for k in count(0))
A326501_list = list(islice(A326501_gen(),10)) # Chai Wah Wu, Jun 18 2022

Formula

a(n) = 1 + (-1)^n * A001099(n).