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a(n) = Sum_{k=0..n} n^k * binomial(2*n,n-k).
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%I #8 Apr 07 2024 17:43:53

%S 1,3,18,146,1510,19302,296520,5339924,110447046,2581169510,

%T 67274981356,1934941601628,60878718397276,2080009638726684,

%U 76694241037743300,3035502492679964520,128364744764608411718,5776084128332328033798,275565308510875579650348

%N a(n) = Sum_{k=0..n} n^k * binomial(2*n,n-k).

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

%F a(n) ~ exp(2) * n^n. - _Vaclav Kotesovec_, Apr 07 2024

%o (PARI) a(n) = sum(k=0, n, n^k*binomial(2*n, n-k));

%Y Cf. A371826, A371827.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 07 2024