%I #10 Dec 29 2023 08:06:58
%S 0,1,10,60,364,2745,27246,346864,5422264,100449225,2149062490,
%T 52097910876,1410401518692,42153624499441,1378058477508454,
%U 48900582823143360,1871456346915007216,76821658841556480753,3366451935514051046802,156839738363103277783900
%N a(n) = Sum_{k=1..n} k^3 * n^(n-k).
%F a(n) = [x^n] x * (1+4*x+x^2)/((1-n*x) * (1-x)^4).
%F a(n) = n * (n^n * (n^2 + 4*n + 1) - n^5 - 3*n^2 - n - 1)/(n-1)^4 for n > 1.
%o (PARI) a(n) = sum(k=1, n, k^3*n^(n-k));
%Y Cf. A062805, A368505, A368524.
%Y Cf. A368527.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Dec 28 2023