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A046919 Maximal coefficient of polynomial p(n), with p(3)=1, p(n) = (1 - t^(2*n - 4))*(1 - t^(2*n - 3))*p(n - 1)/((1 - t^(n - 3))*(1 - t^n)). 4
1, 1, 3, 8, 24, 73, 227, 734, 2430, 8150, 27718, 95514, 332578, 1168261, 4136477, 14749992, 52925886, 190973410, 692583902, 2523265494, 9231352260, 33901898722, 124940568222, 461938289518, 1713007181342, 6369928427268, 23747917426918, 88747514693530, 332397792962692, 1247582980566935, 4691740496135919, 17676678143316236, 66714895880626460, 252207367615436780 (list; graph; refs; listen; history; text; internal format)
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

N. J. A. Sloane, Table of n, a(n) for n = 3..50

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.]

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-Fran├žois Alcover, Aug 01 2013, after Maple *)

CROSSREFS

Cf. A000571, A046918, A210726.

Sequence in context: A006365 A178543 A188175 * A275856 A046342 A238977

Adjacent sequences:  A046916 A046917 A046918 * A046920 A046921 A046922

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Corrected terms and Maple program. - N. J. A. Sloane, May 09 2012

STATUS

approved

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Last modified December 8 15:08 EST 2016. Contains 278945 sequences.