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 A174129 Numerators of the first column of the table of fractions generated by the Akiyama-Tanigawa transform from a first row A164555(k)/A027642(k). 2
 1, 1, -1, -1, 31, 7, -1051, -201, 56911, 18311, -24346415, -4227881, 425739604981, 2082738855, -759610463437, -1935668684041, 91825384886337407, 3104887811293639, -333936446105326262497, -8039608511660213481, 496858217433153341005061 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The first 6 rows if the table generated by iterative application of the Akiyama-Tanigawa transform starting with a header row of fractions  A164555(k)/A027642(k) are:   1, 1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, 0, -691/2730, 0, 7/6, ...   1/2, 2/3, 1/2, 2/15, -1/6, -1/7, 1/6, 4/15, -3/10, -25/33, 5/6, 1382/455, ...   -1/6, 1/3, 11/10, 6/5, -5/42, -13/7, -7/10, 68/15, 453/110, -175/11, ...   -1/2, -23/15, -3/10, 554/105, 365/42, -243/35, -1099/30, 548/165, 19827/110, ...   31/30, -37/15, -1171/70, -478/35, 469/6, 1247/7, -6153/22, -46708/33, ...   7/2, 599/21, -129/14, -38566/105, -20995/42, 211515/77, 524699/66, ... The numerators of the leftmost column define the current sequence. LINKS D. Merlini, R. Sprugnoli, M. C. Verri, The Akiyama-Tanigawa Transformation, Integers, 5 (1) (2005) #A05. MAPLE read("transforms3") ; A174129 := proc(n) Lin := [bernoulli(0), -bernoulli(1), seq(bernoulli(k), k=2..n+1)] ; for r from 1 to n do Lin := AKIYATANI(Lin) ; end do; numer(op(1, Lin)) ; end proc: MATHEMATICA a[0, k_] := a[0, k] = BernoulliB[k]; a[0, 1] = 1/2; a[n_, k_] := a[n, k] = (k+1)*(a[n-1, k] - a[n-1, k+1]); a[n_] := a[n, 0] // Numerator; Table[a[n], {n, 0, 20}] (* Jean-François Alcover_, Aug 14 2012 *) CROSSREFS Cf. A141056 (denominators), A174110, A174111 (first row). Sequence in context: A040939 A040937 A187810 * A305663 A040936 A029821 Adjacent sequences:  A174126 A174127 A174128 * A174130 A174131 A174132 KEYWORD frac,sign AUTHOR Paul Curtz, Mar 09 2010 STATUS approved

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Last modified September 22 16:50 EDT 2020. Contains 337291 sequences. (Running on oeis4.)