A342168 a(n) = U(n, (n+3)/2) where U(n, x) is a Chebyshev polynomial of the 2nd kind.

1, 4, 24, 204, 2255, 30744, 499121, 9409960, 202176360, 4878316860, 130651068911, 3846719565780, 123517560398401, 4296240885694576, 160935647131239840, 6460088606857290384, 276655979838719058119, 12591439417867717440180, 606947064800948702246681

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, A342167.

Programs

Mathematica

Table[ChebyshevU[n, (n + 3)/2], {n, 0, 18}] (* Amiram Eldar, Apr 27 2021 *)

PARI

a(n) = polchebyshev(n, 2, (n+3)/2);

PARI

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

PARI

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

Formula

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).

a(n) ~ exp(3) * n^n. - Vaclav Kotesovec, May 06 2021