A367257 a(n) = Sum_{k=0..n} binomial(n, k) * binomial(n - 1, n - k - 1) * (-n)^k.
1, 1, -3, 10, -15, -474, 12565, -258572, 5136705, -102255290, 2019481101, -37521627252, 543274535089, 1220679586140, -663297992874075, 45545891767647976, -2512550066073884415, 129402386434475858502, -6511375580923238310755, 325739815788711661063900
Offset: 0
Keywords
Links
- Paolo Xausa, Table of n, a(n) for n = 0..350
Programs
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Maple
a := n -> JacobiP(n, 0, -2*n, 1 + 2*n): seq(simplify(a(n)), n = 0..19);
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Mathematica
A367257[n_] := JacobiP[n, 0, -2*n, 2*n+1]; Array[A367257, 25, 0] (* Paolo Xausa, Jan 31 2024 *)
Formula
a(n) = Sum_{k=0..n} A367270(n, k) * (-n)^k.
a(n) = JacobiP(n, 0, -2*n, 1 + 2*n).