A323118 a(n) = U_{n}(n) where U_{n}(x) is a Chebyshev polynomial of the second kind.

1, 2, 15, 204, 3905, 96030, 2883167, 102213944, 4178507265, 193501094490, 10011386405999, 572335117886532, 35827847605137601, 2437406399741075126, 179059769134174484415, 14127079203550978667760, 1191321539697176278429697, 106935795565608726499866930

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..351

Wikipedia, Chebyshev polynomials.

Formula

a(n) = Sum_{k=0..floor(n/2)} (n^2-1)^k*n^(n-2*k) * binomial(n+1,2*k+1).

a(n) ~ 2^n * n^n. - Vaclav Kotesovec, Jan 05 2019

a(n) = Sum_{k=0..n} (2*n-2)^(n-k) * binomial(2*n+1-k,k) = Sum_{k=0..n} (2*n-2)^k * binomial(n+1+k,2*k+1). - Seiichi Manyama, Mar 03 2021

Mathematica

Table[ChebyshevU[n, n], {n, 0, 20}] (* Vaclav Kotesovec, Jan 05 2019 *)

Prog

(PARI) a(n) = polchebyshev(n, 2, n);
(PARI) a(n) = sum(k=0, n\2, (n^2-1)^k*n^(n-2*k)*binomial(n+1, 2*k+1));
(PARI) a(n) = sum(k=0, n, (2*n-2)^k*binomial(n+1+k, 2*k+1)); \\ Seiichi Manyama, Mar 03 2021

Crossrefs

Main diagonal of A323182.

Cf. A115066, A318192, A323117, A349073, A349074, A349075, A349076.

Sequence in context: A351920 A319466 A020557 * A184361 A351501 A124558

Adjacent sequences: A323115 A323116 A323117 * A323119 A323120 A323121

Keyword

nonn

Author

Seiichi Manyama, Jan 05 2019

Status

approved