A368488 a(n) = Sum_{k=0..n} n^k * binomial(k+n-1,k).
1, 2, 17, 334, 10417, 442276, 23690809, 1530206742, 115636017473, 10004657077468, 974950612575601, 105653682110368492, 12602144701834193521, 1640558582759557298696, 231448351542446473323113, 35173958220088874039434726, 5728588740444710703061240065
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n, n^k*binomial(k+n-1, k));
Formula
a(n) = [x^n] 1/((1-x) * (1-n*x)^n).
a(n) ~ 2^(2*n-1) * n^(n - 1/2) / sqrt(Pi). - Vaclav Kotesovec, Dec 27 2023