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A058645
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2^(n-3)*n^2*(n+3).
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5
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0, 1, 10, 54, 224, 800, 2592, 7840, 22528, 62208, 166400, 433664, 1105920, 2768896, 6823936, 16588800, 39845888, 94699520, 222953472, 520486912, 1205862400, 2774532096, 6343884800, 14422114304, 32614907904, 73400320000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) is the number of ways to select a subset of {1,2,...n} and then use the subset as an alphabet to form ordered triples.
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REFERENCES
| A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, Gordon and Breach Science Publishers, 1986-1992.
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FORMULA
| Sum(i^3 * binomial(n, i), i=0..n) = 2^(n-3)*n^2*(n+3).
G.f.: x*(1+2*x-2*x^2)/(1-2*x)^4. E.g.f.: x*(1+3*x+x^2)*e^(2*x).
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MATHEMATICA
| CoefficientList[Series[(x+3x^2+x^3) Exp[x]^2, {x, 0, 20}], x] * Table[n!, {n, 0, 20}]
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PROG
| (PARI) a(n)=if(n<0, 0, 2^(n-3)*n^2*(n+3))
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CROSSREFS
| First differences are in A084903.
Sequence in context: A161755 A053347 A036600 * A170940 A057586 A198770
Adjacent sequences: A058642 A058643 A058644 * A058646 A058647 A058648
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KEYWORD
| nonn
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AUTHOR
| Yong Kong (ykong(AT)curagen.com), Dec 26 2000
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