A052768 a(n) = n*(n-1)*(n-2)*(n-3) for n>=5.

0, 0, 0, 0, 0, 120, 360, 840, 1680, 3024, 5040, 7920, 11880, 17160, 24024, 32760, 43680, 57120, 73440, 93024, 116280, 143640, 175560, 212520, 255024, 303600, 358800, 421200, 491400, 570024, 657720, 755160, 863040, 982080, 1113024

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Comments

Old name was: A simple grammar.

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 725
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Essentially the same as A052762.

Programs

Maple

spec := [S,{B=Set(Z,1 <= card),S=Prod(Z,Z,Z,Z,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Formula

a(n)=0, n <= 4; a(n) = n*(n-1)*(n-2)*(n-3), n >= 5.

G.f.: 24*x^5*(5-10*x+10*x^2-5*x^3+x^4)/(1-x)^5. - Colin Barker, Jun 25 2012

Extensions

More terms and corrected formula from Larry Reeves (larryr(AT)acm.org), Jan 23 2001