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%I #20 Dec 12 2022 16:56:34
%S 1,1,1,2,3,5,9,16,31,61,125,266,579,1305,3009,7120,17255,42697,108005,
%T 278466,731883,1958589,5331625,14758720,41501135,118507301,343405709,
%U 1009313322,3007557523,9081204849,27775308049,86014412384,269603741111,855012176081
%N a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^k.
%F G.f.: Sum_{k>=0} x^k / (1 - k * x^2).
%F a(n) ~ sqrt(Pi) * (n/LambertW(exp(1)*n))^((n + 1 - n/LambertW(exp(1)*n))/2) / sqrt(1 + LambertW(exp(1)*n)). - _Vaclav Kotesovec_, Apr 14 2022
%t Join[{1},Table[Sum[(n-2k)^k,{k,0,Floor[n/2]}],{n,40}]] (* _Harvey P. Dale_, Dec 12 2022 *)
%o (PARI) a(n) = sum(k=0, n\2, (n-2*k)^k);
%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k*x^2)))
%Y Cf. A026898, A104872, A352946.
%Y Cf. A087811.
%K nonn,easy
%O 0,4
%A _Seiichi Manyama_, Apr 09 2022
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