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A253946
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a(n) = 6*binomial(n+1, 6).
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7
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6, 42, 168, 504, 1260, 2772, 5544, 10296, 18018, 30030, 48048, 74256, 111384, 162792, 232560, 325584, 447678, 605682, 807576, 1062600, 1381380, 1776060, 2260440, 2850120, 3562650, 4417686, 5437152, 6645408, 8069424, 9738960, 11686752, 13948704, 16564086
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OFFSET
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5,1
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COMMENTS
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For a set of integers {1, 2, ..., n}, a(n) is the sum of the 3 smallest elements of each subset with 5 elements, which is 6*C(n+1, 6) (for n >= 5), hence a(n) = 6*C(n+1, 6) = 6 * A000579(n+1).
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LINKS
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FORMULA
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a(n) = 6*C(n+1,6) = 6*A000579(n+1).
Sum_{n>=5} 1/a(n) = 1/5.
Sum_{n>=5} (-1)^(n+1)/a(n) = 32*log(2) - 661/30. (End)
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EXAMPLE
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For A = {1, 2, 3, 4, 5, 6} the subsets with 5 elements are {1, 2, 3, 4, 5}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 5, 6}, {1, 3, 4, 5, 6}, {2, 3, 4, 5, 6}.
The sum of 3 smallest elements of each subset: a(6) = (1 + 2 + 3) + (1 + 2 + 3) + (1 + 2 + 3) + (1 + 2 + 4) + (1 + 3 + 4) + (2 + 3 + 4) = 42 = 6*C(6 + 1, 6) = 6*A000579(6+1).
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MAPLE
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MATHEMATICA
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Drop[Plus @@ Flatten[Part[#, 1 ;; 3] & /@ Subsets[Range@ #, {5}]] & /@
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {6, 42, 168, 504, 1260, 2772, 5544}, 40] (* Harvey P. Dale, May 14 2019 *)
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PROG
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(PARI) Vec(6*x^5/(1-x)^7 + O(x^100)) \\ Colin Barker, Apr 03 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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