cp's OEIS Frontend

A229557 Array read by antidiagonals. Rows are the denominators of consecutive harmonic transforms starting with a first row 1, 1, 1,....

%I A229557 #14 Oct 06 2013 09:26:48
%S A229557 1,1,1,1,1,1,1,1,2,1,1,1,6,3,1,1,1,12,33,5,1,1,1,60,825,365,8,1,1,1,
%T A229557 20,113025,810665,5992,13,1,1,1,140,5538225,286794631705,5886103384,
%U A229557 164541,21,1,1,1,280,60920475,5619905141583441965,4630449259971272605672,14469935305431,1031079,34,1,1,1
%N A229557 Array read by antidiagonals. Rows are the denominators of consecutive harmonic transforms starting with a first row 1, 1, 1,....
%C A229557 The "harmonic transform" of a sequence of positive numbers a(i) is the sequence h(n) of the partial sums of their reciprocals: h(n)=sum_{i=1..n} 1/a(i).
%e A229557 Table begins
%e A229557 1, 1,   1,      1,...
%e A229557 1, 1,   1,      1,...
%e A229557 1, 2,   6,     12,...
%e A229557 1, 3,  33,    825,...
%e A229557 1, 5, 365, 810665,...
%p A229557 A229556A := proc(n,k)
%p A229557     option remember;
%p A229557     if n = 1 then
%p A229557         1;
%p A229557     else
%p A229557         add( 1/procname(n-1,c),c=1..k) ;
%p A229557     end if;
%p A229557 end proc:
%p A229557 A229557 := proc(n,k)
%p A229557     denom(A229556A(n,k)) ;
%p A229557 end proc:
%p A229557 for d from 2 to 12 do
%p A229557     for k from d-1 to 1 by -1 do
%p A229557         printf("%d,",A229557(d-k,k)) ;
%p A229557     end do:
%p A229557 end do:
%Y A229557 Cf. A229556 (numerators).
%Y A229557 Rows 1-4 are A000012(n), A000012(n), A002805(n), A124432(n+1).
%Y A229557 Columns 1-2 are A000012(n), A000045(n+1).
%K A229557 nonn,tabl,frac
%O A229557 1,9
%A A229557 _Franz Vrabec_, Sep 26 2013