login
The OEIS is supported by the many generous donors to the OEIS 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 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A034862 a(n) = n!*(3*n^2 - 15*n + 10)/6, n > 4. 1
4, 200, 3360, 43680, 551040, 7136640, 96768000, 1383782400, 20916403200, 334183449600, 5637529497600, 100255034880000, 1876076826624000, 36872930045952000, 759748346413056000, 16381540188389376000, 368990137906790400000, 8668429855133368320000, 212061470640708648960000 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 4..445

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

FORMULA

(3*n^2-21*n+28)*a(n) - n*(3*n^2-15*n+10)*a(n-1) = 0. - R. J. Mathar, Apr 03 2017

E.g.f.: x^4*(1 +7*x +x^2 -3*x^3)/(6*(1-x)^3). - G. C. Greubel, Feb 22 2018

a(n) = A034861(n), n>=5. - R. J. Mathar, Apr 14 2018

MATHEMATICA

Join[{4}, Table[n!*(3*n^2 -15*n +10)/6, {n, 5, 30}]] (* or *) Drop[With[ {nn=50}, CoefficientList[ Series[x^4*(1+7*x+x^2-3*x^3)/(6*(1-x)^3), {x, 0, nn}], x]*Range[0, nn]!], 4] (* G. C. Greubel, Feb 22 2018 *)

PROG

(PARI) for(n=4, 30, print1(if(n==4, 4, n!*(3*n^2 -15*n +10)/6), ", ")) \\ G. C. Greubel, Feb 22 2018

(Magma) [4] cat [Factorial(n)*(3*n^2 -15*n +10)/6: n in [5..30]]; // G. C. Greubel, Feb 22 2018

CROSSREFS

Sequence in context: A297061 A156235 A356214 * A174776 A216932 A317273

Adjacent sequences: A034859 A034860 A034861 * A034863 A034864 A034865

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 08:36 EST 2022. Contains 358605 sequences. (Running on oeis4.)