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A367272
a(n) = Sum_{k=0..n} binomial(n, k)^2 * k^(n - k).
0
1, 1, 5, 28, 209, 1826, 18217, 203106, 2487361, 33077566, 473318201, 7234847126, 117435618577, 2014339775800, 36360190887217, 688237505878726, 13618646813974785, 280960214041690038, 6028928694559721305, 134277542969681115870, 3098232871805383942801
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} binomial(n, k) * A059297(n, k).
log(a(n)) ~ n*(log(n) - log(log(n)) - 1 + (3*log(log(n)) + 2)/log(n) - 1/log(n)^2). - Vaclav Kotesovec, Nov 12 2023
MAPLE
a := n -> add(binomial(n, k)^2*k^(n - k), k = 0 .. n):
seq(a(n), n = 0..22);
MATHEMATICA
Join[{1}, Table[Sum[Binomial[n, k]^2 * k^(n-k), {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Nov 12 2023 *)
CROSSREFS
Cf. A059297.
Sequence in context: A292426 A347005 A356025 * A317968 A107875 A340904
KEYWORD
nonn
AUTHOR
Peter Luschny, Nov 11 2023
STATUS
approved