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A229557
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Array read by antidiagonals. Rows are the denominators of consecutive harmonic transforms starting with a first row 1, 1, 1,....
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2
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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
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,9
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COMMENTS
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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).
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LINKS
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EXAMPLE
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Table begins
1, 1, 1, 1,...
1, 1, 1, 1,...
1, 2, 6, 12,...
1, 3, 33, 825,...
1, 5, 365, 810665,...
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MAPLE
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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:
denom(A229556A(n, k)) ;
end proc:
for d from 2 to 12 do
for k from d-1 to 1 by -1 do
end do:
end do:
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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