A194506 Denominator of the third row of the inverse Akiyama-Tanigawa algorithm from 1/n.

3, 12, 120, 360, 1008, 20160, 259200, 907200, 6652800, 19160064, 39626496000, 62270208000, 603542016000, 640493568000, 1067062284288000, 4001483566080000, 4174096582656000, 162193467211776000, 13651830701752320000, 481714597618974720000

Offset: 0

Author

Paul Curtz, Aug 27 2011

Keywords

• nonn
• frac

Comments

For the numerator sequence and detailed information see A193546.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200
• Iaroslav V. Blagouchine, Three notes on Ser's and Hasse's representation for the zeta-functions, Integers (2018) 18A, Article #A3.

Crossrefs

Cf. A193546 (numerator).

Programs

Mathematica

a[n_, 0] := 1/(n+1); a[n_, m_] := a[n, m] = a[n, m-1] - a[n+1, m-1]/m; a[n_] := a[2, n]; Table[a[n] , {n, 0, 19}] // Denominator (* Jean-François Alcover, Sep 18 2012 *)
Numerator@Table[(-1)^n (n + 1) Integrate[FunctionExpand[x Binomial[x, n + 1]], {x, 0, 1}], {n, 0, 20}] (* Vladimir Reshetnikov, Feb 01 2017 *)

Formula

a(n)/A194506(n) = (-1)^n * (n+1) * Integral_{x=0..1} x*binomial(x,n+1). - Vladimir Reshetnikov, Feb 01 2017