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A342380
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Expansion of e.g.f. (exp(x)-1)*(exp(x) - x^4/24 - x^3/6 - x^2/2 - x - 1).
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1
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0, 0, 0, 0, 0, 0, 6, 28, 92, 255, 637, 1485, 3301, 7098, 14912, 30826, 63018, 127857, 258095, 519251, 1042379, 2089604, 4185194, 8377704, 16764264, 33539155, 67090961, 134196873, 268411297, 536843070, 1073709892, 2147447190, 4294925846, 8589887653, 17179816227
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OFFSET
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0,7
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COMMENTS
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a(n) is the number of binary strings of length n that contain at least five 0's but not all digits are 0.
a(n) is also the number of proper subsets with at least five elements of an n-element set.
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LINKS
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FORMULA
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a(n) = 2^n - Sum_{i={0..4,n}} binomial(n,i).
G.f.: x^6*(2*x^4-9*x^3+16*x^2-14*x+6)/((2*x-1)*(x-1)^5). - Alois P. Heinz, Mar 09 2021
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EXAMPLE
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a(9) = 255 since the strings are the 126 permutations of 000001111, the 84 permutations of 000000111, the 36 permutations of 000000011, and the 9 permutations of 000000001.
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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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STATUS
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approved
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