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

1, 1, 3, 9, 41, 257, 2209, 27009, 455553, 10831873, 360452609, 16786663425, 1102243190785, 101146710556673, 13109796072955905, 2379217548538511361, 609386444958743363585, 219178211386515281412097, 111098724276069341895720961, 79284929294467154275606200321

Offset: 0

Author

Seiichi Manyama, Feb 17 2023

Keywords

• nonn

Crossrefs

Cf. A117402, A360592, A360696, A360705.

Cf. A000684.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x*(1+2^k*x))^k))

PARI

a(n) = sum(k=0, n\2, 2^(k*(n-k))*binomial(n-k, k));

Formula

a(n) = Sum_{k=0..floor(n/2)} 2^(k*(n-k)) * binomial(n-k,k).