A368488 - OEIS

%I #13 Dec 27 2023 07:44:38

%S 1,2,17,334,10417,442276,23690809,1530206742,115636017473,

%T 10004657077468,974950612575601,105653682110368492,

%U 12602144701834193521,1640558582759557298696,231448351542446473323113,35173958220088874039434726,5728588740444710703061240065

%N a(n) = Sum_{k=0..n} n^k * binomial(k+n-1,k).

%F a(n) = [x^n] 1/((1-x) * (1-n*x)^n).

%F a(n) ~ 2^(2*n-1) * n^(n - 1/2) / sqrt(Pi). - _Vaclav Kotesovec_, Dec 27 2023

%o (PARI) a(n) = sum(k=0, n, n^k*binomial(k+n-1, k));

%Y Main diagonal of A368487.

%Y Cf. A000984, A072547.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Dec 26 2023