A360774 - OEIS

%I #9 Feb 20 2023 07:50:49

%S 1,1,5,31,284,3390,49878,871465,17620450,404554997,10394845097,

%T 295485704544,9205957047661,311922101632409,11419004058232897,

%U 449146827324857447,18889836751306735360,845892838094616177138,40182354573647684880446

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

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

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

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

%Y Cf. A360775, A360776.

%Y Cf. A360611, A360618.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 20 2023