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%I #11 Aug 23 2021 13:54:28
%S 1,3,11,57,397,3487,37519,484437,7353473,129104523,2589967603,
%T 58757627185,1493762354293,42223299711159,1318186323111959,
%U 45185985199663629,1691822823829309801,68865092213424362659,3034735030143197197435,144238580771432519823465,7368717925255301486594525
%N a(n) = Sum_{k=1..n} (k^2 + k)^(n-k).
%C Row sums of triangle A261642.
%F a(n)^(1/n) ~ n^2/(exp(2)*LambertW(n)^2). - _Vaclav Kotesovec_, Aug 28 2015
%e Initial terms begin:
%e a(1) = 2^0 = 1;
%e a(2) = 2^1 + 6^0 = 3;
%e a(3) = 2^2 + 6^1 + 12^0 = 11;
%e a(4) = 2^3 + 6^2 + 12^1 + 20^0 = 57;
%e a(5) = 2^4 + 6^3 + 12^2 + 20^1 + 30^0 = 397;
%e a(6) = 2^5 + 6^4 + 12^3 + 20^2 + 30^1 + 42^0 = 3487; ...
%t Table[Sum[(k^2+k)^(n-k),{k,n}],{n,30}] (* _Harvey P. Dale_, Aug 23 2021 *)
%o (PARI) {a(n) = sum(k=1,n, (k + k^2)^(n-k))}
%o for(n=1,30,print1(a(n),", "))
%Y Cf. A261642.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Aug 27 2015
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