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Search: id:A058645
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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
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OFFSET
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0,3
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REFERENCES
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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
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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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PROGRAM
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(PARI) a(n)=if(n<0, 0, 2^(n-3)*n^2*(n+3))
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CROSSREFS
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First differences are in A084903.
Sequence in context: A152762 A053347 A036600 this_sequence A057586 A139610 A088404
Adjacent sequences: A058642 A058643 A058644 this_sequence A058646 A058647 A058648
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KEYWORD
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nonn
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AUTHOR
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Yong Kong (ykong(AT)curagen.com), Dec 26 2000
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