A367257 - OEIS

%I #19 Jan 31 2024 08:06:51

%S 1,1,-3,10,-15,-474,12565,-258572,5136705,-102255290,2019481101,

%T -37521627252,543274535089,1220679586140,-663297992874075,

%U 45545891767647976,-2512550066073884415,129402386434475858502,-6511375580923238310755,325739815788711661063900

%N a(n) = Sum_{k=0..n} binomial(n, k) * binomial(n - 1, n - k - 1) * (-n)^k.

%H Paolo Xausa, <a href="/A367257/b367257.txt">Table of n, a(n) for n = 0..350</a>

%F a(n) = Sum_{k=0..n} A367270(n, k) * (-n)^k.

%F a(n) = JacobiP(n, 0, -2*n, 1 + 2*n).

%p a := n -> JacobiP(n, 0, -2*n, 1 + 2*n): seq(simplify(a(n)), n = 0..19);

%t A367257[n_] := JacobiP[n, 0, -2*n, 2*n+1];

%t Array[A367257, 25, 0] (* _Paolo Xausa_, Jan 31 2024 *)

%Y Cf. A367270, A367256.

%K sign

%O 0,3

%A _Peter Luschny_, Nov 11 2023