A034864 a(5) = 5, a(6) = 1170, for n >= 7, a(n) = n!*(4*n^3 - 30*n^2 + 40*n + 3)/24.

5, 1170, 38850, 757680, 12836880, 212133600, 3554258400, 61372080000, 1100366467200, 20555914579200, 400638734496000, 8148554878464000, 172878910364160000, 3823017399032832000, 88035572875041792000, 2108819186504110080000, 52489556713659985920000

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