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a(n) = Sum_{k=0..n} (-k)^k.
2

%I #28 Jun 18 2022 12:13:25

%S 1,0,4,-23,233,-2892,43764,-779779,15997437,-371423052,9628576948,

%T -275683093663,8640417354593,-294234689237660,10817772136320356,

%U -427076118244539019,18019667955465012597,-809220593930871751580,38537187481365665823844

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

%H Seiichi Manyama, <a href="/A326501/b326501.txt">Table of n, a(n) for n = 0..386</a>

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

%p a:= proc(n) option remember; `if`(n<0, 0, (-n)^n+a(n-1)) end:

%p seq(a(n), n=0..23); # _Alois P. Heinz_, Sep 12 2019

%t RecurrenceTable[{a[0] == 1, a[n] == a[n-1] + (-n)^n}, a, {n, 0, 23}] (* _Jean-François Alcover_, Nov 27 2020 *)

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

%o (Python)

%o from itertools import accumulate, count, islice

%o def A326501_gen(): # generator of terms

%o yield from accumulate((-k)**k for k in count(0))

%o A326501_list = list(islice(A326501_gen(),10)) # _Chai Wah Wu_, Jun 18 2022

%Y Cf. A001099, A062970, A177885.

%K sign,easy

%O 0,3

%A _Seiichi Manyama_, Sep 12 2019