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A368510
a(n) = Sum_{k=0..n} n^(n-k) * binomial(k+n,k).
0
1, 3, 16, 113, 1026, 11782, 166776, 2825349, 55797790, 1258065866, 31866312336, 895430095738, 27632885411236, 928823226029532, 33772464199743184, 1320627875038128045, 55259636489069057910, 2463499964955575965954, 116560977980742613228704
OFFSET
0,2
FORMULA
a(n) = [x^n] 1/((1-n*x) * (1-x)^(n+1)).
a(n) ~ exp(1) * n^n. - Vaclav Kotesovec, Dec 28 2023
PROG
(PARI) a(n) = sum(k=0, n, n^(n-k)*binomial(n+k, k));
CROSSREFS
Sequence in context: A124537 A355720 A305133 * A074523 A329113 A042437
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 28 2023
STATUS
approved