login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085356 a(n) = polygorial(n,3)/polygorial(3,n), n >= 3. 8
1, 5, 45, 630, 12600, 340200, 11907000, 523908000, 28291032000, 1838917080000, 141596615160000, 12743695364400000, 1325344317897600000, 157715973829814400000, 21291656467024944000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..220

Daniel Dockery, Polygorials, Special "Factorials" of Polygonal Numbers.

FORMULA

a(n) = polygorial(n+3, 3)/polygorial(3, n+3) = (n+1)!^2*(n+2)*(n+3)*(n+4)/(2^n*24) = A067550(n+2)/2.

a(n) ~ (1/12)*Pi*n^(2*n+6)/(2^n*exp(2*n)). - Ilya Gutkovskiy, Dec 17 2016

MAPLE

a := n->(n+1)!^2*(n+2)*(n+3)*(n+4)/2^n/24; [seq(a(j), j=0..15)];

seq(mul(binomial(k, 2)-binomial(k, 1), k =5..n), n=4..18 ); # Zerinvary Lajos, Aug 07 2007

MATHEMATICA

polygorial[k_, n_] := FullSimplify[ n!/2^n (k -2)^n*Pochhammer[2/(k -2), n]]; Array[ polygorial[3, #]/polygorial[#, 3] &, 17, 3] (* Robert G. Wilson v, Dec 13 2016 *)

CROSSREFS

Cf. A067550, A084939, A084940, A084941, A084942, A084943, A084944.

Sequence in context: A201365 A112940 A294332 * A113382 A304919 A132688

Adjacent sequences:  A085353 A085354 A085355 * A085357 A085358 A085359

KEYWORD

easy,nonn,changed

AUTHOR

Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003

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 February 21 10:49 EST 2019. Contains 320372 sequences. (Running on oeis4.)