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A059338
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a(n) = sum (from k=1 to n) k^5*(n choose k).
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3
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1, 34, 342, 2192, 11000, 47232, 181888, 646144, 2156544, 6848000, 20877824, 61526016, 176171008, 492126208, 1345536000, 3610247168, 9526771712, 24769069056, 63546720256, 161087488000, 403925630976, 1002841309184
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Finding a closed form for the sum was Problem 541 in the Fall 2000 issue of The Pentagon (official journal of Kappa Mu Epsilon).
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,200
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FORMULA
| The closed form comes from starting with (1+x)^n and repeatedly differentiating and multiplying by x. After five differentiations, substitute x=1 and get a(n) = 2^(n-5)*n^2*(n^3+10n^2+15n-10)
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MAPLE
| with(combinat): for n from 1 to 70 do printf(`%d, `, sum(k^5*binomial(n, k), k=1..n)) od:
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PROG
| (PARI) { for (n = 1, 200, write("b059338.txt", n, " ", sum(k=1, n, k^5*binomial(n, k))); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 26 2009]
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CROSSREFS
| Sequence in context: A160146 A101092 A034978 * A202413 A168122 A135243
Adjacent sequences: A059335 A059336 A059337 * A059339 A059340 A059341
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KEYWORD
| nonn,easy
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AUTHOR
| Pat Costello (matcostello(AT)acs.eku.edu), Jan 26 2001
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 29 2001
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