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 A058645 a(n) = 2^(n-3)*n^2*(n+3). 6
 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; text; internal format)
 OFFSET 0,3 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. 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. LINKS Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16). FORMULA a(n) = Sum_{k=0..n} k^3 * binomial(n, k): binomial transform of A000578. 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). MATHEMATICA CoefficientList[Series[(x+3x^2+x^3) Exp[x]^2, {x, 0, 20}], x] * Table[n!, {n, 0, 20}] PROG (PARI) a(n)=2^(n-3)*n^2*(n+3) CROSSREFS First differences are in A084903. Sequence in context: A267172 A266764 A036600 * A170940 A057586 A213120 Adjacent sequences:  A058642 A058643 A058644 * A058646 A058647 A058648 KEYWORD nonn,easy AUTHOR Yong Kong (ykong(AT)curagen.com), Dec 26 2000 STATUS approved

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