A230340
Denominator of Sum_{k=1..n} 1/(k(k+1)(k+2)(k+3)) = Sum_{k=1..n} 1/Pochhammer(k,4).
Original entry on oeis.org
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
1/(1*2*3*4) + 1/(2*3*4*5) + 1/(3*4*5*6) = 19/360, so a(3) = 360.
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[Denominator(1/18 - 1/(3*(n+1)*(n+2)*(n+3))):n in [0..100]]; // Marius A. Burtea, Jul 30 2019
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a[n_] := Denominator[1/18 - 1/(3*(n+1)*(n+2)*(n+3))]; Table[a[n], {n, 0, 100}]
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a(n) = denominator(1/18 - 1/(3*(n+1)*(n+2)*(n+3))) \\ Colin Barker, Jul 30 2019
A300298
Numerators of r(n) := Sum_{k=0..n-1} 1/Product_{j=0..4} (k + j + 1), for n >= 0, with r(0) = 0.
Original entry on oeis.org
0, 1, 7, 17, 23, 125, 209, 329, 247, 119, 125, 341, 1819, 793, 3059, 3875, 1211, 187, 1219, 4427, 10625, 12649, 4983, 17549, 10237, 11875, 6851, 1311, 35959, 40919, 46375, 17453, 7363, 16511, 36907, 41125, 30463, 101269, 111929, 123409
Offset: 0
The sum begins: 0 + 1/(1*2*3*4*5) + 1/(2*3*4*5*6) + ... = 0 + 1/120 + 1/720 + 1/2520 + 1/6720 + 1/15120 + 1/30240 + ...
The rationals r(n) (partial sums) begin: 0/1, 1/120, 7/720, 17/1680, 23/2240, 125/12096, 209/20160, 329/31680, 247/23760, 119/11440, 125/12012, 341/32760, ...
- L. B. W. Jolley, Summation of Series, Dover Publications, 2nd rev. ed., 1961, p. 38, (201).
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List(List([0..40],n->Sum([0..n-1],k->1/(Product([0..4],j->k+j+1)))),NumeratorRat); # Muniru A Asiru, Apr 05 2018
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[Numerator(n*(50+35*n+10*n^2+n^3)/(96*(1+n)*(2+n)*(n+3)*(4+n))): n in [0..50]]; // Vincenzo Librandi, Apr 06 2018
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Table[Numerator[n (50 + 35 n + 10 n^2 + n^3) / (96 (1 + n) (2 + n) (n + 3) (4 + n))], {n, 0, 50}] (* Vincenzo Librandi, Apr 06 2018 *)
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a(n) = numerator(sum(k=0, n-1, prod(j=0, 4, (k+j+1))^(-1))); \\ Altug Alkan, Apr 05 2018
Showing 1-2 of 2 results.
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