A225749 Triangle T(n,k) giving numerator of integral_{x=0..1} B(n,x)*B(k,x) dx, B = Bernoulli polynomial, n >= 1, 1 <= k <= n.

1, 0, 1, -1, 0, 1, 0, -1, 0, 1, 1, 0, -1, 0, 5, 0, 1, 0, -1, 0, 691, -1, 0, 1, 0, -691, 0, 7, 0, -1, 0, 691, 0, -1, 0, 3617, 1, 0, -691, 0, 1, 0, -3617, 0, 43867, 0, 691, 0, -1, 0, 3617, 0, -43867, 0, 174611, -691, 0, 1, 0, -3617, 0, 43867, 0, -174611, 0, 854513, 0, -1, 0, 3617, 0, -43867, 0, 174611, 0, -77683, 0, 236364091

Offset

0,15

Links

Vincenzo Librandi, Rows n = 0..100, flattened

NIST Digital Library of Mathematical Functions, Bernoulli Polynomials

Eric Weisstein's MathWorld, Bernoulli Polynomial

Example

Triangle begins:
1;
0, 1;
-1, 0, 1;
0, -1, 0, 1;
1, 0, -1, 0, 5;
0, 1, 0, -1, 0, 691;
etc.

Mathematica

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

Crossrefs

Cf. A225750 (denominators)

Sequence in context: A068385 A318657 A286277 * A227985 A071086 A339208

Adjacent sequences: A225746 A225747 A225748 * A225750 A225751 A225752

Keyword

sign,frac,tabl

Author

Jean-François Alcover, May 14 2013

Status

approved