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a(n) = Sum_{k=0..n} (2*k)^k.
4

%I #19 Dec 08 2021 06:48:37

%S 1,3,19,235,4331,104331,3090315,108503819,4403471115,202762761483,

%T 10442762761483,594761064172811,37115108500229387,2518267981703965963,

%U 184577387811646500107,14533484387811646500107,1223459304002440821206283,109651494909968373175414027

%N a(n) = Sum_{k=0..n} (2*k)^k.

%C Partial sums of A062971.

%H Seiichi Manyama, <a href="/A349962/b349962.txt">Table of n, a(n) for n = 0..351</a>

%F a(n) ~ 2^n * n^n. - _Vaclav Kotesovec_, Dec 07 2021

%t a[n_] := Sum[If[k == 0, 1, (2*k)^k], {k, 0, n}]; Array[a, 18, 0] (* _Amiram Eldar_, Dec 07 2021 *)

%o (PARI) a(n) = sum(k=0, n, (2*k)^k);

%Y Cf. A062970, A062971, A349961, A349963, A349970.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Dec 07 2021