OFFSET
3,3
COMMENTS
a(n) is also the number of partitions of n(n-1)/2 into n (nonzero) parts, none greater than n-2 [Riordan].
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 3..200 (terms 3..50 from N. J. A. Sloane)
J. Riordan, The number of score sequences in tournaments, J. Combin. Theory, 5 (1968), 87-89. [The main result of this paper seems to be wrong - compare A000571 and A210726.]
FORMULA
a(n) ~ sqrt(3) * 2^(2*n-3) / (Pi * n^2). - Vaclav Kotesovec, Jan 07 2023
EXAMPLE
1; 1+t+t^2+t^3+t^4+t^5, t^10+t^9+2*t^8+2*t^7+3*t^6+3*t^5+3*t^4+2*t^3+2*t^2+t+1, ...
MAPLE
p := proc(n)
option remember;
if n = 3 then 1 else
simplify((1-t^(2*n-4))*(1-t^(2*n-3))*p(n-1)/((1-t^(n-3))*(1-t^n)));
fi; end;
for i from 3 to 40 do
lprint(coeff(expand(p(i)), t, i*(i-3)/2)):
od:
MATHEMATICA
p[3] = 1; p[n_] := p[n] = (1 - t^(2*n-4))*(1 - t^(2*n-3))*(p[n-1]/((1 - t^(n-3))*(1 - t^n)))// Simplify // Expand; a[n_] := Coefficient[p[n], t, n*(n-3)/2]; Table[a[n], {n, 3, 40}] (* Jean-François Alcover, Aug 01 2013, after Maple *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
Corrected terms and Maple program. - N. J. A. Sloane, May 09 2012
STATUS
approved