OFFSET
0,7
COMMENTS
Original name: a simple grammar.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 742
Index entries for linear recurrences with constant coefficients, signature (30,-395,3000,-14523,46710,-100805,143700,-129076,65760,-14400).
FORMULA
E.g.f.: x*exp(x)^5-5*x*exp(x)^4+10*exp(x)^3*x-10*exp(x)^2*x+5*x*exp(x)-x.
Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, ( - 14400 - 27000*n^2 - 32880*n - 120*n^5 - 1800*n^4 - 10200*n^3)*a(n) + (42196*n^2 + 19454*n^3 + 32880*n + 274*n^5 + 3836*n^4)*a(n + 1) + ( - 13500*n - 13275*n^3 - 24075*n^2 - 225*n^5 - 2925*n^4)*a(n + 2) + (85*n^5 + 3400*n + 1020*n^4 + 4165*n^3 + 6630*n^2)*a(n + 3) + ( - 915*n^2 - 450*n - 615*n^3 - 15*n^5 - 165*n^4)*a(n + 4) + (n^5 + 10*n^4 + 35*n^3 + 50*n^2 + 24*n)*a(n + 5)}.
From Andrew Howroyd, Aug 08 2020: (Start)
a(n) = n*A001118(n-1) for n > 1.
G.f.: 120*x^6*(2 - 5*x)*(3 - 30*x + 95*x^2 - 100*x^3 + 24*x^4)/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x))^2.
E.g.f.: x*(exp(x) - 1)^5. (End)
MAPLE
spec := [S, {B=Set(Z, 1 <= card), S=Prod(Z, B, B, B, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
A052785[n_] := If[n == 0, 0, 120*n*StirlingS2[n-1, 5]];
Array[A052785, 25, 0] (* Paolo Xausa, Jun 04 2026 *)
PROG
(PARI) a(n)={if(n>=1, 5!*n*stirling(n-1, 5, 2), 0)} \\ Andrew Howroyd, Aug 08 2020
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
INRIA Encyclopedia of Combinatorial Structures, Jan 25 2000
EXTENSIONS
Name changed and terms a(21) and beyond from Andrew Howroyd, Aug 08 2020
STATUS
approved