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A229556 Array read by antidiagonals. Rows are the numerators of consecutive harmonic transforms starting with a first row 1, 1, 1, ....

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