The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A174129

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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).
(history; published version)

#28 by N. J. A. Sloane at Fri Feb 18 23:09:01 EST 2022

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proposed

approved

#27 by Michel Marcus at Wed Jan 12 05:57:13 EST 2022

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editing

proposed

#26 by Michel Marcus at Wed Jan 12 05:56:26 EST 2022

CROSSREFS

Cf. A164555, A027642, A048993.

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proposed

editing

Discussion

Wed Jan 12

05:57

Michel Marcus: yes and added new xrefs

#25 by Fabián Pereyra at Fri Jan 07 03:23:50 EST 2022

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editing

proposed

#24 by Fabián Pereyra at Fri Jan 07 03:23:45 EST 2022

FORMULA

a(n) = numerator(Sum_{j=0..n} (-1)^(n-j)*j!*S2Stirling2(n,j)*B(j)), where B are the Bernoulli numbers A164555/A027642. - Fabián Pereyra, Jan 06 2022

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proposed

editing

#23 by Fabián Pereyra at Thu Jan 06 18:08:10 EST 2022

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editing

proposed

#22 by Fabián Pereyra at Thu Jan 06 17:48:30 EST 2022

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 *)

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proposed

editing

#21 by Michel Marcus at Thu Jan 06 17:32:05 EST 2022

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editing

proposed

#20 by Michel Marcus at Thu Jan 06 17:32:02 EST 2022

LINKS

D. Merlini, R. Sprugnoli, and M. C. Verri, <a href="https://www.emis.de/journals/INTEGERS/papers/f5/f5.Abstract.html">The Akiyama-Tanigawa Transformation</a>, Integers, 5 (1) (2005) #A05.

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proposed

editing

#19 by Fabián Pereyra at Thu Jan 06 16:58:52 EST 2022

STATUS

editing

proposed