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

Author

Paul Curtz, Jul 18 2011

Keywords

• nonn
• frac

Comments

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

Examples

			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, ...
		

Links

• 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.

Crossrefs

Cf. A194531 (numerators).

Programs

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 *)