A225750 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.

12, 1, 180, 120, 1, 840, 1, 630, 1, 2100, 252, 1, 1680, 1, 16632, 1, 840, 1, 2772, 1, 2522520, 240, 1, 1584, 1, 2162160, 1, 20592, 1, 594, 1, 1351350, 1, 2574, 1, 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

Offset

0,1

Links

Vincenzo Librandi, Rows n = 0..99, flattened

NIST Digital Library of Mathematical Functions, Bernoulli Polynomials

Eric Weisstein's MathWorld, Bernoulli Polynomial

Example

Triangle begins:
12;
1, 180;
120, 1, 840;
1, 630, 1, 2100;
252, 1, 1680, 1, 16632;
1, 840, 1, 2772, 1, 2522520;
etc.

Mathematica

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

Crossrefs

Cf. A225749 (numerators).

Sequence in context: A265825 A347492 A038327 * A157780 A223514 A232627

Adjacent sequences: A225747 A225748 A225749 * A225751 A225752 A225753

Keyword

nonn,frac,tabl

Author

Jean-François Alcover, May 14 2013

Status

approved