A368525 a(n) = Sum_{k=1..n} k^3 * n^(n-k).
0, 1, 10, 60, 364, 2745, 27246, 346864, 5422264, 100449225, 2149062490, 52097910876, 1410401518692, 42153624499441, 1378058477508454, 48900582823143360, 1871456346915007216, 76821658841556480753, 3366451935514051046802, 156839738363103277783900
Offset: 0
Programs
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PARI
a(n) = sum(k=1, n, k^3*n^(n-k));
Formula
a(n) = [x^n] x * (1+4*x+x^2)/((1-n*x) * (1-x)^4).
a(n) = n * (n^n * (n^2 + 4*n + 1) - n^5 - 3*n^2 - n - 1)/(n-1)^4 for n > 1.