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Numerators of inverse of triangle A082985(n).
0

%I #16 Oct 13 2013 22:37:13

%S 1,-1,1,2,-1,1,-8,1,-2,1,8,-4,11,-10,1,-32,8,-5,29,-5,1,6112,-8,26,

%T -33,7,-7,1,-3712,512,-112,313,-100,602,-28,1,362624,-2944,1936,-1816,

%U 593,-1268,70,-4,1,-71706112,2432,-960,31568,-1481,9681,-566,38,-15,1

%N Numerators of inverse of triangle A082985(n).

%C First column of the example: A212196(n)/A181131(n), main diagonal of A164555(n)/A027642(n). See A190339(n). Hence a link between Chebyshev and Bernoulli numbers.

%C Mirror image of A201453.

%F T(k,m) = numerator of F(k,m) = (1/(2*m-2*k+1)) * sum(i=0..2*k, binomial(m,2*k-i)*binomial(2*m-2*k+i,i) * Bernoulli(i)). - _Ralf Stephan_, Oct 10 2013

%e Numerators of

%e 1,

%e -1/3, 1/3,

%e 2/15, -1/3, 1/5,

%e -8/105, 1/3, -2/5, 1/7,

%e 8/105, -4/9, 11/15, -10/21, 1/9,

%e -32/231, 8/9, -5/3, 29/21, -5/9, 1/11

%t rows = 10; u[n_, m_] /; m > n = 0; u[n_, m_] := Binomial[2*n - m, m]*(2*n + 1)/(2*n - 2*m + 1); t = Table[u[n, m], {n, 0, rows - 1}, {m, 0, rows - 1}] // Inverse; Table[t[[n, k]] // Numerator, {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Oct 08 2013 *)

%Y Cf. A201453(n)/A201454(n), A098435.

%K sign,frac,tabl

%O 0,4

%A _Paul Curtz_, Oct 08 2013

%E More terms from _Jean-François Alcover_, Oct 08 2013