A360776 - OEIS

%I #9 Feb 20 2023 07:50:28

%S 1,1,4,27,257,3129,46683,823799,16780342,387467154,10000823639,

%T 285328449077,8916487888186,302885106945216,11112292144568909,

%U 437902806653498835,18447046953316227905,827251374022851280231,39346845973273509115167

%N Expansion of Sum_{k>=0} (x * (k + x^3))^k.

%F a(n) = Sum_{k=0..floor(n/4)} (n-3*k)^(n-4*k) * binomial(n-3*k,k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x*(k+x^3))^k))

%o (PARI) a(n) = sum(k=0, n\4, (n-3*k)^(n-4*k)*binomial(n-3*k, k));

%Y Cf. A360774, A360775.

%Y Cf. A360032, A360728.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 20 2023