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A065551
Triangle of Faulhaber numbers (numerators) read by rows.
2
1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 0, -3, 3, -1, 1, 0, 5, -5, 17, -2, 1, 0, -691, 691, -118, 41, -5, 1, 0, 35, -35, 359, -44, 14, -1, 1, 0, -3617, 3617, -1237, 1519, -293, 22, -7, 1, 0, 43867, -43867, 750167, -13166, 2829, -2258, 217, -4, 1, 0, -1222277, 1222277, -627073, 1540967, -198793, 689, -235, 46, -3, 1
OFFSET
0,12
COMMENTS
From Wolfdieter Lang, Jun 25 2011: (Start)
In the Gessel and Viennot reference f(n,k) = a(n,k)/A065553(n,k), n>=0, k>=0.
(n+1)*f(n,k) = A(n+1,n-k), with Knuth's A(m,k) =
A093556(m,k)/A093557(m,k). See the Knuth reference given in A093556, and the W. Lang link. (End)
LINKS
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)=numerator(f(n,k)).
EXAMPLE
Triangle begins:
{1},
{0, 1},
{0, -1, 1},
{0, 1, -1, 1},
{0, -3, 3, -1, 1},
{0, 5, -5, 17, -2, 1}.
CROSSREFS
Cf. A065553.
Cf. A103438.
Sequence in context: A065547 A143333 A283798 * A283797 A059441 A186028
KEYWORD
frac,sign,tabl
AUTHOR
Wouter Meeussen, Dec 02 2001
STATUS
approved