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%I #10 Sep 01 2022 05:00:08
%S 1,1,2,29,3699,10625002,607758784933,868305359018619811,
%T 72322260589630363186583012,141134946941935843819745493472571577,
%U 21506852953850913182859127590586670415329232127,213131394708948856925732826175269041102801068792839463406106
%N a(n) = Sum_{k=0..n} Stirling2(n,k)^n.
%H G. C. Greubel, <a href="/A345041/b345041.txt">Table of n, a(n) for n = 0..34</a>
%t Table[Sum[StirlingS2[n, k]^n, {k, 0, n}], {n, 0, 11}]
%o (PARI) a(n) = sum(k=0, n, stirling(n, k, 2)^n) \\ _Felix Fröhlich_, Jun 06 2021
%o (Magma) [(&+[StirlingSecond(n,j)^n: j in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Aug 31 2022
%o (SageMath)
%o def A345041(n): return sum(stirling_number2(n,j)^n for j in (0..n))
%o [A345041(n) for n in (0..20)] # _G. C. Greubel_, Aug 31 2022
%Y Cf. A000110, A008277, A047797, A048993, A167010, A345040.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jun 06 2021
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