%I #26 Jun 13 2022 03:03:30
%S 1,1,1,1,2,1,1,3,3,1,1,4,11,5,1,1,5,25,73,8,1,1,6,137,2221,749,13,1,1,
%T 7,49,353777,1964654,12657,21,1,1,8,363,19595573,786674809783,
%U 14862065179,343693,34,1,1,9,761,239046803,17003676861538314284,13379715149864207035877,35955580499839
%N Array read by antidiagonals. Rows are the numerators of consecutive harmonic transforms starting with a first row 1, 1, 1, ....
%C 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 Table begins
%e 1, 1, 1, 1, ...
%e 1, 2, 3, 4, ...
%e 1, 3, 11, 25, ...
%e 1, 5, 73, 2221, ...
%e 1, 8, 749, 1964654, ...
%e which are the numerators of
%e 1, 1, 1, 1, 1, ...
%e 1, 2, 3, 4, 5, ...
%e 1, 3/2, 11/6, 25/12, 137/60, ...
%e 1, 5/3, 73/33, 2221/825, 353777/113025, ...
%e 1, 8/5, 749/365, 1964654/810665, 786674809783/286794631705, ...
%p A229556A := proc(n,k)
%p option remember;
%p if n = 1 then
%p 1;
%p else
%p add( 1/procname(n-1,c),c=1..k) ;
%p end if;
%p end proc:
%p A229556 := proc(n,k)
%p numer(A229556A(n,k)) ;
%p end proc:
%p for d from 2 to 12 do
%p for k from d-1 to 1 by -1 do
%p printf("%d,",A229556(d-k,k)) ;
%p end do:
%p end do:
%Y Cf. A229557 (denominators).
%Y Rows 1-4 are A000012(n), A000027(n), A001008(n), A096987(n+1).
%Y Columns 1-2 are A000012(n), A000045(n+2).
%Y Column 3 gives A350834.
%K nonn,tabl,frac
%O 1,5
%A _Franz Vrabec_, Sep 26 2013