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

Author

Seiichi Manyama, Mar 03 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..386
• Spencer Daugherty, Pamela E. Harris, Ian Klein, and Matt McClinton, Metered Parking Functions, arXiv:2406.12941 [math.CO], 2024. See pp. 11, 22.
• Wikipedia, Chebyshev polynomials.

Crossrefs

Cf. A097690, A097691, A323118, A342168.

Programs

Mathematica

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

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));

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