This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342167 #31 Jun 28 2024 01:20:30
%S A342167 1,3,15,115,1189,15456,242047,4435929,93149001,2205405829,58130412911,
%T A342167 1688353631328,53577891882061,1844491975179855,68470281953483775,
%U A342167 2726406212682669391,115921586524134874897,5241862216131004082160,251197634537351883217999
%N A342167 a(n) = U(n, (n+2)/2) where U(n, x) is a Chebyshev polynomial of the 2nd kind.
%H A342167 Seiichi Manyama, <a href="/A342167/b342167.txt">Table of n, a(n) for n = 0..386</a>
%H A342167 Spencer Daugherty, Pamela E. Harris, Ian Klein, and Matt McClinton, <a href="https://arxiv.org/abs/2406.12941">Metered Parking Functions</a>, arXiv:2406.12941 [math.CO], 2024. See pp. 11, 22.
%H A342167 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.
%F A342167 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).
%F A342167 a(n) ~ exp(2) * n^n. - _Vaclav Kotesovec_, May 06 2021
%t A342167 Table[ChebyshevU[n, (n + 2)/2], {n, 0, 18}] (* _Amiram Eldar_, Apr 27 2021 *)
%o A342167 (PARI) a(n) = polchebyshev(n, 2, (n+2)/2);
%o A342167 (PARI) a(n) = sum(k=0, n, n^(n-k)*binomial(2*n+1-k, k));
%o A342167 (PARI) a(n) = sum(k=0, n, n^k*binomial(n+1+k, 2*k+1));
%Y A342167 Cf. A097690, A097691, A323118, A342168.
%K A342167 nonn
%O A342167 0,2
%A A342167 _Seiichi Manyama_, Mar 03 2021