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

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, 20, 113025, 810665, 5992, 13, 1, 1, 1, 140, 5538225, 286794631705, 5886103384, 164541, 21, 1, 1, 1, 280, 60920475, 5619905141583441965, 4630449259971272605672, 14469935305431, 1031079, 34, 1, 1, 1

Offset

1,9

Comments

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).

Links

Table of n, a(n) for n=1..57.

Example

Table begins
1, 1,   1,      1,...
1, 1,   1,      1,...
1, 2,   6,     12,...
1, 3,  33,    825,...
1, 5, 365, 810665,...

Maple

A229556A := proc(n, k)
    option remember;
    if n = 1 then
        1;
    else
        add( 1/procname(n-1, c), c=1..k) ;
    end if;
end proc:
A229557 := proc(n, k)
    denom(A229556A(n, k)) ;
end proc:
for d from 2 to 12 do
    for k from d-1 to 1 by -1 do
        printf("%d, ", A229557(d-k, k)) ;
    end do:
end do:

Crossrefs

Cf. A229556 (numerators).

Rows 1-4 are A000012(n), A000012(n), A002805(n), A124432(n+1).

Columns 1-2 are A000012(n), A000045(n+1).

Sequence in context: A300830 A139329 A335432 * A332700 A256268 A213275

Adjacent sequences: A229554 A229555 A229556 * A229558 A229559 A229560

Keyword

nonn,tabl,frac

Author

Franz Vrabec, Sep 26 2013

Status

approved