A230069 Numerators of inverse of triangle A082985(n).

1, -1, 1, 2, -1, 1, -8, 1, -2, 1, 8, -4, 11, -10, 1, -32, 8, -5, 29, -5, 1, 6112, -8, 26, -33, 7, -7, 1, -3712, 512, -112, 313, -100, 602, -28, 1, 362624, -2944, 1936, -1816, 593, -1268, 70, -4, 1, -71706112, 2432, -960, 31568, -1481, 9681, -566, 38, -15, 1

Offset: 0

Author

Paul Curtz, Oct 08 2013

Keywords

• sign
• frac
• tabl

Comments

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.

Mirror image of A201453.

Examples

			Numerators of
1,
-1/3,    1/3,
2/15,   -1/3,   1/5,
-8/105,  1/3,  -2/5,    1/7,
8/105,  -4/9, 11/15, -10/21,  1/9,
-32/231, 8/9,  -5/3,  29/21, -5/9, 1/11
		

Crossrefs

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

Programs

Mathematica

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 *)

Formula

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

Extensions

More terms from Jean-François Alcover, Oct 08 2013