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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved