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A062970 a(n) = 1 + Sum_{j=1..n} j^j.

%I A062970 #24 Jun 17 2022 16:05:56
%S A062970 1,2,6,33,289,3414,50070,873613,17650829,405071318,10405071318,
%T A062970 295716741929,9211817190185,312086923782438,11424093749340454,
%U A062970 449317984130199829,18896062057839751445,846136323944176515622,40192544399240714091046,2018612200059554303215025
%N A062970 a(n) = 1 + Sum_{j=1..n} j^j.
%C A062970 The usual convention in the OEIS is that 0^0 = 1. This sequence could therefore be defined as Sum_{j=0..n} j^j. See also A001923.
%H A062970 T. D. Noe, <a href="/A062970/b062970.txt">Table of n, a(n) for n = 0..100</a>
%F A062970 a(n) = a(n-1) + A000312(n) = A001923(n) + 1.
%F A062970 a(n) ~ n^n. - _Vaclav Kotesovec_, Nov 27 2017
%e A062970 a(4) = 1 + 1^1 + 2^2 + 3^3 + 4^4 = 1 + 1 + 4 + 27 + 256 = 289.
%t A062970 Table[Sum[Sum[Binomial[n, k] StirlingS2[n, k] k!, {k, 0, n}], {n, 0, m}], {m, 0, 20}] (* _Geoffrey Critzer_, Mar 18 2009 *)
%t A062970 Join[{1},Accumulate[Table[n^n,{n,20}]]+1] (* _Harvey P. Dale_, Aug 31 2016 *)
%o A062970 (PARI) { a=0; for (n=0, 100, write("b062970.txt", n, " ", a+=n^n) ) } \\ _Harry J. Smith_, Aug 14 2009
%o A062970 (Python)
%o A062970 from itertools import count, accumulate, islice
%o A062970 def A062970_gen(): # generator of terms
%o A062970     yield from accumulate((k**k for k in count(1)),initial=1)
%o A062970 A062970_list = list(islice(A062970_gen(),20)) # _Chai Wah Wu_, Jun 17 2022
%Y A062970 Cf. A000312, A001923.
%K A062970 nonn
%O A062970 0,2
%A A062970 _Henry Bottomley_, Jul 23 2001