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A230069 Numerators of inverse of triangle A082985(n). 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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.

LINKS

Table of n, a(n) for n=0..54.

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

EXAMPLE

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

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 *)

CROSSREFS

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

Sequence in context: A294605 A060865 A078689 * A276813 A134470 A119418

Adjacent sequences:  A230066 A230067 A230068 * A230070 A230071 A230072

KEYWORD

sign,frac,tabl

AUTHOR

Paul Curtz, Oct 08 2013

EXTENSIONS

More terms from Jean-François Alcover, Oct 08 2013

STATUS

approved

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Last modified August 21 10:36 EDT 2018. Contains 313937 sequences. (Running on oeis4.)