The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A322904 a(n) = Sum_{k=0..n} binomial(2*n+1,2*k+1)*(n^2-1)^(n-k)*n^(2*k). 2
 1, 1, 181, 38081, 14526601, 8943235489, 8138661470941, 10287228590683393, 17254778510170993681, 37095265466946847758401, 99474891266913130060486021, 325534304813775692747248543681, 1276941308627620432293188401109401, 5914558735952850788377566338591400673 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..193 Wikipedia, Chebyshev polynomials. FORMULA For n > 0, a(n) = (1/n) * T_{2*n+1}(n) where T_{n}(x) is a Chebyshev polynomial of the first kind. For n > 0, a(n) = (1/n) * cosh((2*n+1)*arccosh(n)). a(n) ~ 4^n * n^(2*n). - Vaclav Kotesovec, Jan 03 2019 MATHEMATICA a[0] = 1; a[n_] := 1/n ChebyshevT[2n+1, n]; Table[a[n], {n, 0, 13}] (* Jean-François Alcover, Jan 02 2019 *) PROG (PARI) {a(n) = sum(k=0, n, binomial(2*n+1, 2*k+1)*(n^2-1)^(n-k)*n^(2*k))} (PARI) a(n) = if (n==0, 1, polchebyshev(2*n+1, 1, n)/n); \\ Michel Marcus, Jan 02 2019 (MAGMA) [&+[Binomial(2*n+1, 2*k+1)*(n^2-1)^(n-k)*n^(2*k): k in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Jan 03 2019 CROSSREFS Diagonal of A188646. Cf. A253880, A302329, A302330, A302331, A302332. Sequence in context: A224991 A189342 A189778 * A107075 A228134 A066626 Adjacent sequences:  A322901 A322902 A322903 * A322905 A322906 A322907 KEYWORD nonn AUTHOR Seiichi Manyama, Dec 30 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 26 07:25 EST 2020. Contains 338632 sequences. (Running on oeis4.)