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

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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

Prog

(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));

Crossrefs

Cf. A117402, A360592, A360696, A360705.

Cf. A000684.

Sequence in context: A074502 A109743 A139150 * A293955 A113271 A249045

Adjacent sequences: A360701 A360702 A360703 * A360705 A360706 A360707

Keyword

nonn

Author

Seiichi Manyama, Feb 17 2023

Status

approved