A367256 a(n) = Sum_{k=0..n} binomial(n, k) * binomial(n - 1, k - 1) * n^(n - k).
1, 1, 5, 46, 593, 9726, 192637, 4457580, 117769409, 3492894070, 114790042901, 4137157889316, 162154385331985, 6863637142316332, 311905306734621069, 15140756439172826776, 781693659313991730945, 42759819036520142319270, 2469943332976774829606821
Offset: 0
Keywords
Links
- Paolo Xausa, Table of n, a(n) for n = 0..350
Programs
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Maple
a := n -> if n= 0 then 1 else n*n^(n - 1)*hypergeom([1 - n, 1 - n], [2], 1/n) fi: seq(simplify(a(n)), n = 0..19);
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Mathematica
A367256[n_] := If[n == 0, 1, n*n^(n-1)*Hypergeometric2F1[1-n, 1-n, 2, 1/n]]; Array[A367256, 25, 0] (* Paolo Xausa, Jan 31 2024 *)
Formula
a(n) = Sum_{k=0..n} A367267(n, k) * n^(n - k).
a(n) = n*n^(n - 1)*hypergeom([1 - n, 1 - n], [2], 1/n) for n > 0.
a(n) ~ exp(2*sqrt(n) - 1) * n^(n - 3/4) / (2*sqrt(Pi)). - Vaclav Kotesovec, Nov 11 2023