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%I #25 Sep 04 2018 12:41:00
%S 3,12,120,360,1008,20160,259200,907200,6652800,19160064,39626496000,
%T 62270208000,603542016000,640493568000,1067062284288000,
%U 4001483566080000,4174096582656000,162193467211776000,13651830701752320000,481714597618974720000
%N Denominator of the third row of the inverse Akiyama-Tanigawa algorithm from 1/n.
%C For the numerator sequence and detailed information see A193546.
%H Alois P. Heinz, <a href="/A194506/b194506.txt">Table of n, a(n) for n = 0..200</a>
%H Iaroslav V. Blagouchine, <a href="http://math.colgate.edu/~integers/sjs3/sjs3.Abstract.html">Three notes on Ser's and Hasse's representation for the zeta-functions</a>, Integers (2018) 18A, Article #A3.
%F a(n)/A194506(n) = (-1)^n * (n+1) * Integral_{x=0..1} x*binomial(x,n+1). - _Vladimir Reshetnikov_, Feb 01 2017
%t 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 *)
%t Numerator@Table[(-1)^n (n + 1) Integrate[FunctionExpand[x Binomial[x, n + 1]], {x, 0, 1}], {n, 0, 20}] (* _Vladimir Reshetnikov_, Feb 01 2017 *)
%Y Cf. A193546 (numerator).
%K nonn,frac
%O 0,1
%A _Paul Curtz_, Aug 27 2011
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