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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A346515 a(n) = n*(n+2)*(n+4)*(n+6)*(n+8)*(n+10)*(n+12)*(n+14). 1
0, 2027025, 10321920, 34459425, 92897280, 218243025, 464486400, 916620705, 1703116800, 3011753745, 5109350400, 8365982625, 13284311040, 20534684625, 30996725760, 45808142625, 66421555200, 94670161425, 132843110400, 183771489825, 250925875200, 338526428625, 451666575360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

FORMULA

a(n) = A346514(n)^2 - A152691(n+7)^2.

MATHEMATICA

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

CROSSREFS

Cf. A239035, A190577, A346514, A346376.

Sequence in context: A032754 A271768 A104441 * A290037 A289956 A263892

Adjacent sequences:  A346512 A346513 A346514 * A346516 A346517 A346518

KEYWORD

nonn,easy

AUTHOR

Lamine Ngom, Jul 21 2021

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)