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 A342168 #32 Jun 28 2024 01:20:13
%S A342168 1,4,24,204,2255,30744,499121,9409960,202176360,4878316860,
%T A342168 130651068911,3846719565780,123517560398401,4296240885694576,
%U A342168 160935647131239840,6460088606857290384,276655979838719058119,12591439417867717440180,606947064800948702246681
%N A342168 a(n) = U(n, (n+3)/2) where U(n, x) is a Chebyshev polynomial of the 2nd kind.
%H A342168 Seiichi Manyama, <a href="/A342168/b342168.txt">Table of n, a(n) for n = 0..386</a>
%H A342168 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 A342168 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.
%F A342168 a(n) = Sum_{k=0..n} (n+1)^(n-k) * binomial(2*n+1-k,k) = Sum_{k=0..n} (n+1)^k * binomial(n+1+k,2*k+1).
%F A342168 a(n) ~ exp(3) * n^n. - _Vaclav Kotesovec_, May 06 2021
%t A342168 Table[ChebyshevU[n, (n + 3)/2], {n, 0, 18}] (* _Amiram Eldar_, Apr 27 2021 *)
%o A342168 (PARI) a(n) = polchebyshev(n, 2, (n+3)/2);
%o A342168 (PARI) a(n) = sum(k=0, n, (n+1)^(n-k)*binomial(2*n+1-k, k));
%o A342168 (PARI) a(n) = sum(k=0, n, (n+1)^k*binomial(n+1+k, 2*k+1));
%Y A342168 Cf. A097690, A097691, A323118, A342167.
%K A342168 nonn
%O A342168 0,2
%A A342168 _Seiichi Manyama_, Mar 03 2021