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A230340 Denominator of Sum_{k=1..n} 1/(k(k+1)(k+2)(k+3)) = Sum_{k=1..n} 1/Pochhammer(k,4).

%I A230340 #27 Feb 16 2025 08:33:20
%S A230340 1,24,20,360,315,1008,1512,2160,1485,1320,1716,2184,4095,10080,12240,
%T A230340 14688,8721,20520,7980,3080,5313,36432,41400,46800,26325,58968,65772,
%U A230340 8120,13485,9920,98208,107712,58905,128520,139860,151848,27417,59280
%N A230340 Denominator of Sum_{k=1..n} 1/(k(k+1)(k+2)(k+3)) = Sum_{k=1..n} 1/Pochhammer(k,4).
%H A230340 Colin Barker, <a href="/A230340/b230340.txt">Table of n, a(n) for n = 0..1000</a>
%H A230340 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/PochhammerSymbol.html">Pochhammer Symbol</a>
%F A230340 Denominator(1/18 - 1/(3*(n+1)*(n+2)*(n+3))).
%e A230340 1/(1*2*3*4) + 1/(2*3*4*5) + 1/(3*4*5*6) = 19/360, so a(3) = 360.
%t A230340 a[n_] := Denominator[1/18 - 1/(3*(n+1)*(n+2)*(n+3))]; Table[a[n], {n, 0, 100}]
%o A230340 (PARI) a(n) = denominator(1/18 - 1/(3*(n+1)*(n+2)*(n+3))) \\ _Colin Barker_, Jul 30 2019
%o A230340 (Magma) [Denominator(1/18 - 1/(3*(n+1)*(n+2)*(n+3))):n in [0..100]]; // _Marius A. Burtea_, Jul 30 2019
%Y A230340 Cf. A001563, A052762, A094258, A125650, A230328, A230339 (numerators).
%K A230340 nonn,frac,easy
%O A230340 0,2
%A A230340 _Jean-François Alcover_, Oct 16 2013