A342167 a(n) = U(n, (n+2)/2) where U(n, x) is a Chebyshev polynomial of the 2nd kind.

1, 3, 15, 115, 1189, 15456, 242047, 4435929, 93149001, 2205405829, 58130412911, 1688353631328, 53577891882061, 1844491975179855, 68470281953483775, 2726406212682669391, 115921586524134874897, 5241862216131004082160, 251197634537351883217999

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..386

Wikipedia, Chebyshev polynomials.

Formula

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

a(n) ~ exp(2) * n^n. - Vaclav Kotesovec, May 06 2021

Mathematica

Table[ChebyshevU[n, (n + 2)/2], {n, 0, 18}] (* Amiram Eldar, Apr 27 2021 *)

Prog

(PARI) a(n) = polchebyshev(n, 2, (n+2)/2);
(PARI) a(n) = sum(k=0, n, n^(n-k)*binomial(2*n+1-k, k));
(PARI) a(n) = sum(k=0, n, n^k*binomial(n+1+k, 2*k+1));

Crossrefs

Cf. A097690, A097691, A323118, A342168.

Sequence in context: A346224 A082163 A331122 * A346272 A190629 A341647

Adjacent sequences: A342164 A342165 A342166 * A342168 A342169 A342170

Keyword

nonn

Author

Seiichi Manyama, Mar 03 2021

Status

approved