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

0,3

Comments

The numerators are given in A065551. - Wolfdieter Lang, Jun 25 1011

Links

Table of n, a(n) for n=0..77.

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

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

Example

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

Crossrefs

Cf. A065551.

Sequence in context: A337470 A006019 A201146 * A016545 A142977 A356601

Adjacent sequences: A065550 A065551 A065552 * A065554 A065555 A065556

Keyword

frac,nonn,tabl

Author

Wouter Meeussen, Dec 02 2001

Status

approved