This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065551 #16 Jul 04 2020 04:13:23 %S A065551 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, %T A065551 -5,1,0,35,-35,359,-44,14,-1,1,0,-3617,3617,-1237,1519,-293,22,-7,1,0, %U A065551 43867,-43867,750167,-13166,2829,-2258,217,-4,1,0,-1222277,1222277,-627073,1540967,-198793,689,-235,46,-3,1 %N A065551 Triangle of Faulhaber numbers (numerators) read by rows. %C A065551 From _Wolfdieter Lang_, Jun 25 2011: (Start) %C A065551 In the Gessel and Viennot reference f(n,k) = a(n,k)/A065553(n,k), n>=0, k>=0. %C A065551 (n+1)*f(n,k) = A(n+1,n-k), with Knuth's A(m,k) = %C A065551 A093556(m,k)/A093557(m,k). See the Knuth reference given in A093556, and the W. Lang link. (End) %H A065551 Ira M. Gessel and X. G. Viennot, <a href="http://people.brandeis.edu/~gessel/homepage/papers/pp.pdf">Determinants, paths and plane partitions</a>, 1989, p. 27, eqn 12.2 %F A065551 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). %F A065551 a(n,k)=numerator(f(n,k)). %e A065551 Triangle begins: %e A065551 {1}, %e A065551 {0, 1}, %e A065551 {0, -1, 1}, %e A065551 {0, 1, -1, 1}, %e A065551 {0, -3, 3, -1, 1}, %e A065551 {0, 5, -5, 17, -2, 1}. %Y A065551 Cf. A065553. %Y A065551 Cf. A103438. %K A065551 frac,sign,tabl %O A065551 0,12 %A A065551 _Wouter Meeussen_, Dec 02 2001