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!)
A034864 a(5) = 5, a(6) = 1170, for n >= 7, a(n) = n!*(4*n^3 - 30*n^2 + 40*n + 3)/24. 1
5, 1170, 38850, 757680, 12836880, 212133600, 3554258400, 61372080000, 1100366467200, 20555914579200, 400638734496000, 8148554878464000, 172878910364160000, 3823017399032832000, 88035572875041792000, 2108819186504110080000, 52489556713659985920000 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 5..445

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

FORMULA

a(n) = A034863(n), n > 6. - R. J. Mathar, Feb 26 2008

E.g.f.: x^5*(1 + 35*x + 35*x^2 - 59*x^3 + 12*x^5)/(24*(1-x)^4). - G. C. Greubel, Feb 16 2018

MAPLE

[5, 1170, seq(factorial(n)*(4*n^3-30*n^2+40*n+3)/24, n=7..22)]; # Muniru A Asiru, Feb 17 2018

MATHEMATICA

Join[{5, 1170}, Table[n!*(4*n^3-30*n^2+40*n+3)/24, {n, 7, 50}]] (* or *) Drop[With[{nn = 30}, CoefficientList[Series[(x^5*(1+35*x+35*x^2-59*x^3 + 12*x^5))/(24*(1-x)^4), {x, 0, nn}], x]*Range[0, nn]!], 5] (* G. C. Greubel, Feb 16 2018 *)

PROG

(PARI) x='x+O('x^30); Vec(serlaplace(x^5*(1+35*x+35*x^2-59*x^3 +12*x^5)/( 24*(1-x)^4))) \\ G. C. Greubel, Feb 16 2018

(MAGMA) [5, 1170] cat [Factorial(n)*(4*n^3-30*n^2+40*n+3)/24: n in [7..30]]; // G. C. Greubel, Feb 16 2018

(GAP) A034864:=Concatenation([5, 1170], List([7..22], n->Factorial(n)*(4*n^3-30*n^2+40*n+3)/24)); # Muniru A Asiru, Feb 17 2018

CROSSREFS

Sequence in context: A306141 A317374 A189249 * A157642 A234811 A069642

Adjacent sequences:  A034861 A034862 A034863 * A034865 A034866 A034867

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 23:38 EST 2021. Contains 349558 sequences. (Running on oeis4.)