cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

A346515 a(n) = n*(n+2)*(n+4)*(n+6)*(n+8)*(n+10)*(n+12)*(n+14).

Original entry on oeis.org

0, 2027025, 10321920, 34459425, 92897280, 218243025, 464486400, 916620705, 1703116800, 3011753745, 5109350400, 8365982625, 13284311040, 20534684625, 30996725760, 45808142625, 66421555200, 94670161425, 132843110400, 183771489825, 250925875200, 338526428625, 451666575360
Offset: 0

Views

Author

Lamine Ngom, Jul 21 2021

Keywords

Comments

a(n) can always be expressed as the difference of two squares: x^2 - y^2.
A346514(n) gives the x-values for each product. The y-values being A152691(n+7).
More generally, for any k, we have: n*(n+k)*(n+2*k)*...*(n+7*k) = a(n,k) = x(n,k)^2 - y(n,k)^2, where
x(n,k) = n^4 + 14*k*n^3 + 63*k^2*n^2 + 98*k^3*n + 28*k^4,
y(n,k) = 8*k^3*n + 28*k^4.
A239035(n) corresponds to a(n,k) in the case k = 1, with related y(n,k) = A346376(n).

Links

Crossrefs

Cf. A239035, A190577, A346514, A346376.

Programs

  • Mathematica
    a[n_] := (n + 14)!!/(n - 2)!!; Array[a, 23, 0] (* Amiram Eldar, Jul 22 2021 *)

Formula

a(n) = A346514(n)^2 - A152691(n+7)^2.
Showing 1-1 of 1 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.