A368510 a(n) = Sum_{k=0..n} n^(n-k) * binomial(k+n,k).
1, 3, 16, 113, 1026, 11782, 166776, 2825349, 55797790, 1258065866, 31866312336, 895430095738, 27632885411236, 928823226029532, 33772464199743184, 1320627875038128045, 55259636489069057910, 2463499964955575965954, 116560977980742613228704
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, n^(n-k)*binomial(n+k, k));
Formula
a(n) = [x^n] 1/((1-n*x) * (1-x)^(n+1)).
a(n) ~ exp(1) * n^n. - Vaclav Kotesovec, Dec 28 2023