cp's OEIS Frontend

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

%I A065553 #20 Aug 03 2025 03:58:02
%S A065553 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,
%T A065553 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,
%U A065553 55,33,165,66,1,2,3,2,11,1,6,3,20,5,45,15,40,9,10,3,12
%N A065553 Triangle of Faulhaber numbers (denominators) read by rows.
%C A065553 The numerators are given in A065551. - _Wolfdieter Lang_, Jun 25 2011
%H A065553 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 A065553 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 A065553 a(n,k) = denominator(f(n,k)). - _Wolfdieter Lang_, Jun 25 2011
%e A065553 Triangle begins:
%e A065553   {1},
%e A065553   {1, 2},
%e A065553   {1, 6, 3},
%e A065553   {1, 6, 3, 4},
%e A065553   {1, 10, 5, 2, 5},
%e A065553   {1, 6, 3, 12, 3, 6},
%e A065553   ...
%Y A065553 Cf. A065551.
%K A065553 frac,nonn,tabl
%O A065553 0,3
%A A065553 _Wouter Meeussen_, Dec 02 2001