A193220 Denominators of the fourth row of Akiyama-Tanigawa algorithm leading to Bernoulli numbers A164555(n)/A027642(n).

1, 30, 20, 35, 84, 84, 120, 495, 55, 286, 1092, 455, 280, 2040, 816, 969, 855, 1330, 1540, 5313, 1012, 2300, 7800, 2925, 819, 10962, 4060, 4495, 7440, 5456, 5984, 19635, 1785, 7770, 25308, 9139, 4940

Offset

0,2

Comments

Denominators of row k=3 of the table in A051714.

Links

Table of n, a(n) for n=0..36.

M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 3 (2000), #00.2.9.

D. Merlini, R. Sprugnoli, M. C. Verri, The Akiyama-Tanigawa Transformation, Integers, 5 (1) (2005) #A05.

Example

The third row is 0, 1/30, 1/20, 2/35, 5/84, 5/84, 7/120, 28/495, 3/55, 15/286, 55/1092, 22/455, 13/280, ...

Maple

read("transforms3");
L := [seq(1/n, n=1..40)] ;
L1 := AKIYATANI(L) ; L2 := AKIYATANI(L1) ; L3 := AKIYATANI(L2) ;
apply(denom, %) ; # R. J. Mathar, Aug 20 2011

Mathematica

a[0, k_] := 1/(k+1); a[n_, k_] := a[n, k] = (k+1)*(a[n-1, k] - a[n-1, k+1]); Table[a[3, k], {k, 0, 36}] // Denominator (* Jean-François Alcover, Sep 18 2012 *)

Crossrefs

Cf. A194531 (numerators).

Sequence in context: A040873 A070891 A033971 * A040872 A361029 A268855

Adjacent sequences: A193217 A193218 A193219 * A193221 A193222 A193223

Keyword

nonn,frac

Author

Paul Curtz, Jul 18 2011

Status

approved