A360696 - OEIS

%I #10 Feb 16 2023 12:21:59

%S 1,1,2,9,98,3212,428525,165045051,342128248388,2522279110319003,

%T 90930729844450829580,17690430223837969605522024,

%U 13516362920784209950583739768297,79459280482613898608830749440741093093

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

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

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

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

%Y Cf. A000045, A360592, A360684.

%Y Cf. A355463.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 16 2023