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 A229557 Array read by antidiagonals. Rows are the denominators of consecutive harmonic transforms starting with a first row 1, 1, 1,.... 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 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

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Last modified September 15 11:45 EDT 2024. Contains 375938 sequences. (Running on oeis4.)