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A366151
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a(n) = T(n, 3), where T(n, k) = Sum_{i=0..n} i^k * binomial(n, i) * (1/2)^(n-k).
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0
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0, 4, 20, 54, 112, 200, 324, 490, 704, 972, 1300, 1694, 2160, 2704, 3332, 4050, 4864, 5780, 6804, 7942, 9200, 10584, 12100, 13754, 15552, 17500, 19604, 21870, 24304, 26912, 29700, 32674, 35840, 39204, 42772, 46550
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OFFSET
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0,2
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COMMENTS
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A mean of binomials as might occur as the Expectation of random variables.
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LINKS
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FORMULA
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a(n) = n^2*(n + 3).
a(n) = [x^n] (2*x*(2 + 2*x - x^2))/(x - 1)^4.
a(n) = n! * [x^n] exp(x)*(x^3 + 6*x^2 + 4*x).
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MAPLE
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a := n -> n^2*(n + 3): seq(a(n), n = 0..35);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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