cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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)).

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%I A046919 #35 Jan 07 2023 05:40:33
%S A046919 1,1,3,8,24,73,227,734,2430,8150,27718,95514,332578,1168261,4136477,
%T A046919 14749992,52925886,190973410,692583902,2523265494,9231352260,
%U A046919 33901898722,124940568222,461938289518,1713007181342,6369928427268,23747917426918,88747514693530,332397792962692,1247582980566935,4691740496135919,17676678143316236,66714895880626460,252207367615436780
%N 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)).
%C A046919 a(n) is also the number of partitions of n(n-1)/2 into n (nonzero) parts, none greater than n-2 [Riordan].
%H A046919 Vaclav Kotesovec, <a href="/A046919/b046919.txt">Table of n, a(n) for n = 3..200</a> (terms 3..50 from N. J. A. Sloane)
%H A046919 J. Riordan, <a href="http://dx.doi.org/10.1016/S0021-9800(68)80032-8">The number of score sequences in tournaments</a>, J. Combin. Theory, 5 (1968), 87-89. [The main result of this paper seems to be wrong - compare A000571 and A210726.]
%F A046919 a(n) ~ sqrt(3) * 2^(2*n-3) / (Pi * n^2). - _Vaclav Kotesovec_, Jan 07 2023
%e A046919 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, ...
%p A046919 p := proc(n)
%p A046919 option remember;
%p A046919 if n = 3 then 1 else
%p A046919 simplify((1-t^(2*n-4))*(1-t^(2*n-3))*p(n-1)/((1-t^(n-3))*(1-t^n)));
%p A046919 fi; end;
%p A046919 for i from 3 to 40 do
%p A046919 lprint(coeff(expand(p(i)),t,i*(i-3)/2)):
%p A046919 od:
%t A046919 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 *)
%Y A046919 Cf. A000571, A046918, A210726.
%K A046919 nonn,nice
%O A046919 3,3
%A A046919 _N. J. A. Sloane_
%E A046919 Corrected terms and Maple program. - _N. J. A. Sloane_, May 09 2012