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Triangle T(n,k) giving denominator of integral_{x=0..1} B(n,x)*B(k,x) dx, B = Bernoulli polynomial, n >= 1, 1 <= k <= n.
2

%I #11 Jul 19 2013 07:54:22

%S 12,1,180,120,1,840,1,630,1,2100,252,1,1680,1,16632,1,840,1,2772,1,

%T 2522520,240,1,1584,1,2162160,1,20592,1,594,1,1351350,1,2574,1,

%U 6563700,132,1,600600,1,1716,1,5834400,1,38798760,1,180180,1,858,1,4084080,1,34918884,1,60969480,32760,1,312,1,2227680,1,25395552,1,55426800,1,97349616,1,78,1,928200,1,14814072,1,41570100,1,8112468,1,7382345880

%N Triangle T(n,k) giving denominator of integral_{x=0..1} B(n,x)*B(k,x) dx, B = Bernoulli polynomial, n >= 1, 1 <= k <= n.

%H Vincenzo Librandi, <a href="/A225750/b225750.txt">Rows n = 0..99, flattened</a>

%H NIST Digital Library of Mathematical Functions, <a href="http://dlmf.nist.gov/24.13#i">Bernoulli Polynomials</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/BernoulliPolynomial.html">Bernoulli Polynomial</a>

%e Triangle begins:

%e 12;

%e 1, 180;

%e 120, 1, 840;

%e 1, 630, 1, 2100;

%e 252, 1, 1680, 1, 16632;

%e 1, 840, 1, 2772, 1, 2522520;

%e etc.

%t t[n_, k_] := (-1)^(n - 1)*k!*n!/(k + n)!*BernoulliB[k + n]; Table[t[n, k] // Denominator, {n, 1, 12}, {k, 1, n}] // Flatten

%Y Cf. A225749 (numerators).

%K nonn,frac,tabl

%O 0,1

%A _Jean-François Alcover_, May 14 2013