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A360704 Expansion of Sum_{k>=0} (x * (1 + 2^k * x))^k.

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%I A360704 #10 Feb 17 2023 03:19:41
%S A360704 1,1,3,9,41,257,2209,27009,455553,10831873,360452609,16786663425,
%T A360704 1102243190785,101146710556673,13109796072955905,2379217548538511361,
%U A360704 609386444958743363585,219178211386515281412097,111098724276069341895720961,79284929294467154275606200321
%N A360704 Expansion of Sum_{k>=0} (x * (1 + 2^k * x))^k.
%F A360704 a(n) = Sum_{k=0..floor(n/2)} 2^(k*(n-k)) * binomial(n-k,k).
%o A360704 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x*(1+2^k*x))^k))
%o A360704 (PARI) a(n) = sum(k=0, n\2, 2^(k*(n-k))*binomial(n-k, k));
%Y A360704 Cf. A117402, A360592, A360696, A360705.
%Y A360704 Cf. A000684.
%K A360704 nonn
%O A360704 0,3
%A A360704 _Seiichi Manyama_, Feb 17 2023