A368534 a(n) = Sum_{k=1..n} binomial(k+1,2) * n^(n-k).
0, 1, 5, 24, 146, 1215, 13431, 186816, 3130436, 61291125, 1371742105, 34522712136, 964626945558, 29621465864627, 991330604373851, 35906022352657920, 1399219698628043016, 58367293868445147657, 2594796705962971336125, 122463905297217627859000
Offset: 0
Programs
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Mathematica
Table[Sum[Binomial[k+1,2]n^(n-k),{k,n}],{n,0,20}] (* Harvey P. Dale, May 14 2025 *) -
PARI
a(n) = sum(k=1, n, binomial(k+1, 2)*n^(n-k));
Formula
a(n) = [x^n] x/((1-n*x) * (1-x)^3).
a(n) = n * (2*n^(n+1) - n^3 - n^2 + n - 1)/(2 * (n-1)^3) for n > 1.