OFFSET
0,7
COMMENTS
Original name: a simple grammar.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 749
Index entries for linear recurrences with constant coefficients, signature (30,-405,3250,-17247,63690,-167615,316350,-424428,394280,-240480,86400,-13824).
FORMULA
E.g.f.: x^2*exp(x)^4-4*x^2*exp(x)^3+6*x^2*exp(x)^2-4*exp(x)*x^2+x^2.
Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, (1200*n+840*n^2+240*n^3+576+24*n^4)*a(n)+(1200-50*n^4+100*n-850*n^2-400*n^3)*a(n+1)+(210*n^3+175*n^2+35*n^4-420*n)*a(n+2)+(10*n^2-40*n^3+40*n-10*n^4)*a(n+3)+(-n^2+n^4-2*n+2*n^3)*a(n+4)}.
a(n) = n*A052776(n-1) = 4!*n*(n-1)*Stirling2(n-2,4) for n >= 2. - Andrew Howroyd, Aug 08 2020
MAPLE
spec := [S, {B=Set(Z, 1 <= card), S=Prod(Z, Z, B, B, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
PROG
(PARI) a(n)={if(n>=2, 4!*n*(n-1)*stirling(n-2, 4, 2), 0)} \\ Andrew Howroyd, Aug 08 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
Name changed and terms a(21) and beyond from Andrew Howroyd, Aug 08 2020
STATUS
approved