A065553 Triangle of Faulhaber numbers (denominators) read by rows.

1, 1, 2, 1, 6, 3, 1, 6, 3, 4, 1, 10, 5, 2, 5, 1, 6, 3, 12, 3, 6, 1, 210, 105, 21, 15, 6, 7, 1, 2, 1, 12, 3, 3, 1, 8, 1, 30, 15, 6, 15, 9, 3, 6, 9, 1, 42, 21, 420, 15, 10, 35, 20, 3, 10, 1, 110, 55, 33, 165, 66, 1, 2, 3, 2, 11, 1, 6, 3, 20, 5, 45, 15, 40, 9, 10, 3, 12

Offset: 0

Author

Wouter Meeussen, Dec 02 2001

Keywords

• frac
• nonn
• tabl

Comments

The numerators are given in A065551. - Wolfdieter Lang, Jun 25 2011

Examples

			Triangle begins:
  {1},
  {1, 2},
  {1, 6, 3},
  {1, 6, 3, 4},
  {1, 10, 5, 2, 5},
  {1, 6, 3, 12, 3, 6},
  ...
		

Links

• Ira M. Gessel and X. G. Viennot, Determinants, paths and plane partitions, 1989, p. 27, eqn 12.2

Crossrefs

Cf. A065551.

Formula

Sum_{n>=0, k>=0} f(n, k)*t^k*x^(2*n+1)/(2*n+1)! is the expansion of (cosh(sqrt(1+4*t)*x/2)-cosh(x/2))/t/sinh(x/2).

a(n,k) = denominator(f(n,k)). - Wolfdieter Lang, Jun 25 2011