A053126 -id:A053126 - cp's OEIS frontend

A054323 Fifth column of Lanczos triangle A053125 (decreasing powers).

5, 140, 2016, 21120, 183040, 1397760, 9748480, 63504384, 392232960, 2321285120, 13264486400, 73610035200, 398475657216, 2111580405760, 10984378859520, 56221121904640, 283661115064320, 1413061420253184, 6959221409054720

Offset: 0

Wolfdieter Lang

C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.
Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (20, -160, 640, -1280, 1024).

Cf. A053125, A054322.

Bisection of A080951.

List([0..20], n-> 4^n*Binomial(2*n+5, 4)); # G. C. Greubel, Jul 22 2019

[4^n*Binomial(2*n+5, 4): n in [0..20]]; // G. C. Greubel, Jul 22 2019

Table[4^n Binomial[2n+5,4],{n,0,20}] (* or *) LinearRecurrence[{20,-160, 640,-1280,1024},{5,140,2016,21120,183040},20] (* Harvey P. Dale, Mar 03 2018 *)

vector(20, n, n--; 4^n*binomial(2*n+5, 4)) \\ G. C. Greubel, Jul 22 2019

[4^n*binomial(2*n+5, 4) for n in (0..20)] # G. C. Greubel, Jul 22 2019

a(n) = 4^n*binomial(2*n+5, 4) = 4^n*A053126(n+4) = A053125(n+4, 4).
G.f.: (5 +40*x +16*x^2)/(1-4*x)^5.
E.g.f.: (15 +360*x +1464*x^2 +1664*x^3 +512*x^4)*exp(4*x)/3. - G. C. Greubel, Jul 22 2019
a(n) = 20*a(n-1)-160*a(n-2)+640*a(n-3)-1280*a(n-4)+1024*a(n-5). - Wesley Ivan Hurt, May 02 2021

A196790 Binomial coefficients C(2*n-9,10).

Original entry on oeis.org

11, 286, 3003, 19448, 92378, 352716, 1144066, 3268760, 8436285, 20030010, 44352165, 92561040, 183579396, 348330136, 635745396, 1121099408, 1917334783, 3190187286, 5178066751, 8217822536, 12777711870, 19499099620, 29248649430, 43183019880, 62828356305, 90177170226

Offset: 10

Vincenzo Librandi, Oct 07 2011

Vincenzo Librandi, Table of n, a(n) for n = 10..200

Cf. A053126, A053127, A053128, A053129, A053130, A053131, A053132, A053133.

Magma
```
[Binomial(2*n-9,10): n in [10..40]];
```

a[n_] := Binomial[2*n - 9, 10]; Array[a, 20, 10] (* Amiram Eldar, Oct 21 2022 *)

G.f.: x^10*(11+165*x+462*x^2+330*x^3+55*x^4+x^5) / (1-x)^11. - R. J. Mathar, Oct 08 2011
From Amiram Eldar, Oct 21 2022: (Start)
Sum_{n>=10} 1/a(n) = 447187/252 - 2560*log(2).
Sum_{n>=10} (-1)^n/a(n) = 40*Pi + 80*log(2) - 6517/36. (End)

cp's OEIS Frontend

A054323 Fifth column of Lanczos triangle A053125 (decreasing powers).

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