This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A360835 #13 Feb 23 2023 07:37:12 %S A360835 1,1,4,27,258,3221,49572,905466,19122502,458161191,12275530636, %T A360835 363646493044,11801356347294,416365459777150,15867258718677348, %U A360835 649548679156603983,28426564854590132236,1324406974148881529057,65448443631801436742052 %N A360835 Expansion of Sum_{k>=0} (k * x)^k / (1 - (k * x)^3)^(k+1). %F A360835 a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^n * binomial(n-2*k,k). %o A360835 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-(k*x)^3)^(k+1))) %o A360835 (PARI) a(n) = sum(k=0, n\3, (n-3*k)^n*binomial(n-2*k, k)); %Y A360835 Cf. A072034, A360834. %Y A360835 Cf. A000930, A360783, A360788. %K A360835 nonn %O A360835 0,3 %A A360835 _Seiichi Manyama_, Feb 22 2023