A342207 a(n) = U(n,n+1) where U(n,x) is a Chebyshev polynomial of the second kind.

1, 4, 35, 496, 9701, 241956, 7338631, 262184896, 10783446409, 501827040100, 26069206375211, 1495427735314800, 93885489910449901, 6403169506981578436, 471427031236487965199, 37265225545829174607616, 3147895910861898495432209

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..351

Wikipedia, Chebyshev polynomials.

Formula

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

a(n) ~ exp(1) * 2^n * n^n. - Vaclav Kotesovec, Mar 05 2021

Mathematica

Table[ChebyshevU[n, n + 1], {n, 0, 16}] (* Amiram Eldar, Mar 05 2021 *)

Prog

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

Crossrefs

Cf. A107995, A323118, A342168, A342205.

Sequence in context: A242795 A349527 A287886 * A224797 A143669 A349656

Adjacent sequences: A342204 A342205 A342206 * A342208 A342209 A342210

Keyword

nonn

Author

Seiichi Manyama, Mar 05 2021

Status

approved