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A046919
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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)).
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4
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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
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OFFSET
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3,3
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COMMENTS
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a(n) is also the number of partitions of n(n-1)/2 into n (nonzero) parts, none greater than n-2 [Riordan].
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REFERENCES
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J. Riordan, The number of score sequences in tournaments, J. Combin. Theory, 5 (1968), 87-89. [But the paper seems to contain an error - compare A000571 and A210726].
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 3..50
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EXAMPLE
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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, ...
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MAPLE
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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:
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MATHEMATICA
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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))); a[n_] := Max[ CoefficientList[ Series[p[n], {t, 0, n^2}], t]]; Table[a[n], {n, 3, 36}] (* Jean-François Alcover, Jun 18 2012 *)
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CROSSREFS
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Cf. A000571, A046918, A210726.
Sequence in context: A006365 A178543 A188175 * A046342 A182453 A000958
Adjacent sequences: A046916 A046917 A046918 * A046920 A046921 A046922
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Corrected terms and Maple program. - N. J. A. Sloane, May 09 2012
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STATUS
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approved
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