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A342207
a(n) = U(n,n+1) where U(n,x) is a Chebyshev polynomial of the second kind.
2
1, 4, 35, 496, 9701, 241956, 7338631, 262184896, 10783446409, 501827040100, 26069206375211, 1495427735314800, 93885489910449901, 6403169506981578436, 471427031236487965199, 37265225545829174607616, 3147895910861898495432209
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 05 2021
STATUS
approved