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

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..350

Formula

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

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

Maple

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

Mathematica

A367257[n_] := JacobiP[n, 0, -2*n, 2*n+1];
Array[A367257, 25, 0] (* Paolo Xausa, Jan 31 2024 *)

Crossrefs

Cf. A367270, A367256.

Sequence in context: A259877 A182334 A051420 * A092827 A087904 A242203

Adjacent sequences: A367254 A367255 A367256 * A367258 A367259 A367260

Keyword

sign

Author

Peter Luschny, Nov 11 2023

Status

approved