OFFSET
0,7
COMMENTS
a(n) is also the number of forests of 5 labeled rooted trees of height at most 1 with n labels, where any root may contain >= 1 labels.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (45, -835, 8175, -44524, 127860, -151200).
FORMULA
G.f.: x^5/((1-5x)(1-6x)(1-7x)(1-8x)(1-9x)(1-10x)).
E.g.f.: exp(5*x)*((exp(x)-1)^5)/5!.
MAPLE
a := proc(k::nonnegint) local M; M := Matrix(k+1, (i, j)-> if (i=j-1) then 1 elif j=1 then [seq(-1* coeff(product(1-t*x, t=k..2*k), x, u), u=1..k+1)][i] else 0 fi); p-> (M^p)[1, k+1] end(5); seq(a(n), n=0..30);
MATHEMATICA
CoefficientList[Series[x^5/((1-5x)(1-6x)(1-7x)(1-8x)(1-9x)(1-10x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{45, -835, 8175, -44524, 127860, -151200}, {0, 0, 0, 0, 0, 1}, 30] (* Harvey P. Dale, Aug 30 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 12 2008
STATUS
approved