cp's OEIS Frontend

A085841 Triangle: row #n has n+1 terms. T(n,m) = 4^m (2n+1)! / ( (2n-2m)! (2m+1)! ).

%I A085841 #15 Mar 18 2018 14:30:31
%S A085841 1,3,4,5,40,16,7,140,336,64,9,336,2016,2304,256,11,660,7392,21120,
%T A085841 14080,1024,13,1144,20592,109824,183040,79872,4096,15,1820,48048,
%U A085841 411840,1281280,1397760,430080,16384
%N A085841 Triangle: row #n has n+1 terms. T(n,m) = 4^m (2n+1)! / ( (2n-2m)! (2m+1)! ).
%C A085841 Row #n has the unsigned coefficients of a polynomial whose roots are 2 cot (Pi k / (2n+1)) for k=1..2n.
%C A085841 Polynomial of row #n = Sum_{m=0..n} (-1)^m*T(n,m)*x^(2n-2m).
%H A085841 Rui Duarte and António Guedes de Oliveira, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Duarte/duarte7.html">A Famous Identity of Hajós in Terms of Sets</a>, Journal of Integer Sequences, Vol. 17 (2014), #14.9.1.
%e A085841 1
%e A085841 3x^2 - 4
%e A085841 5x^4 - 40x^2 + 16
%e A085841 7x^6 - 140x^4 + 336x^2 - 64
%e A085841 9x^8 - 336x^6 + 2016x^4 - 2304x^2 + 256
%e A085841 11x^10 - 660x^8 + 7392x^6 - 21120x^4 + 14080x^2 - 1024
%e A085841 Polynomial #4 has eight roots: 2 cot (Pi k / 9) for k=1..8.
%o A085841 (PARI) T(n,m) = 4^m*(2*n+1)!/((2*n-2*m)!*(2*m+1)!);
%o A085841 tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print); \\ _Michel Marcus_, Mar 18 2018
%Y A085841 Cf. A085840.
%K A085841 nonn,tabl
%O A085841 0,2
%A A085841 _Gary W. Adamson_, Jul 05 2003
%E A085841 Edited by _Don Reble_, Nov 13 2005