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

1, 24, 20, 360, 315, 1008, 1512, 2160, 1485, 1320, 1716, 2184, 4095, 10080, 12240, 14688, 8721, 20520, 7980, 3080, 5313, 36432, 41400, 46800, 26325, 58968, 65772, 8120, 13485, 9920, 98208, 107712, 58905, 128520, 139860, 151848, 27417, 59280

Offset: 0

Author

Jean-François Alcover, Oct 16 2013

Keywords

• nonn
• frac
• easy

Examples

			1/(1*2*3*4) + 1/(2*3*4*5) + 1/(3*4*5*6) = 19/360, so a(3) = 360.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Eric Weisstein's MathWorld, Pochhammer Symbol

Crossrefs

Cf. A001563, A052762, A094258, A125650, A230328, A230339 (numerators).

Programs

Magma

[Denominator(1/18 - 1/(3*(n+1)*(n+2)*(n+3))):n in [0..100]]; // Marius A. Burtea, Jul 30 2019

Mathematica

a[n_] := Denominator[1/18 - 1/(3*(n+1)*(n+2)*(n+3))]; Table[a[n], {n, 0, 100}]

PARI

a(n) = denominator(1/18 - 1/(3*(n+1)*(n+2)*(n+3))) \\ Colin Barker, Jul 30 2019

Formula

Denominator(1/18 - 1/(3*(n+1)*(n+2)*(n+3))).