A360774 Expansion of Sum_{k>=0} (x * (k + x))^k.

1, 1, 5, 31, 284, 3390, 49878, 871465, 17620450, 404554997, 10394845097, 295485704544, 9205957047661, 311922101632409, 11419004058232897, 449146827324857447, 18889836751306735360, 845892838094616177138, 40182354573647684880446

Offset: 0

Author

Seiichi Manyama, Feb 20 2023

Keywords

• nonn

Crossrefs

Cf. A360775, A360776.

Cf. A360611, A360618.

Programs

PARI

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

PARI

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

Formula

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