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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: A065246 A297061 A156235 * A174776 A216932 A317273

Adjacent sequences:  A034859 A034860 A034861 * A034863 A034864 A034865

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 13 06:38 EDT 2021. Contains 344981 sequences. (Running on oeis4.)