A368489 a(n) = Sum_{k=0..n} n^k * binomial(k+n,k).
1, 3, 31, 643, 20421, 873806, 46994011, 3042431715, 230249448841, 19940350062394, 1944516598602711, 210829412453667998, 25156743053019602701, 3275876521195372322892, 462262670054775645538099, 70264375447526610838701091
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n, n^k*binomial(k+n, k));
Formula
a(n) = [x^n] 1/((1-x) * (1-n*x)^(n+1)).
a(n) ~ 4^n * n^(n - 1/2) / sqrt(Pi). - Vaclav Kotesovec, Dec 27 2023