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%I #10 Feb 20 2023 07:50:45
%S 1,1,4,28,260,3152,46913,826677,16823968,388245283,10016796672,
%T 285699444297,8926107792609,303160590533808,11120927427841820,
%U 438196895219227683,18457860168281435172,827678295600605015006,39364859979651634985089
%N Expansion of Sum_{k>=0} (x * (k + x^2))^k.
%F a(n) = Sum_{k=0..floor(n/3)} (n-2*k)^(n-3*k) * binomial(n-2*k,k).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x*(k+x^2))^k))
%o (PARI) a(n) = sum(k=0, n\3, (n-2*k)^(n-3*k)*binomial(n-2*k, k));
%Y Cf. A360774, A360776.
%Y Cf. A360018, A360727.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Feb 20 2023