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Search: id:A059338
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A059338 a(n) = sum (from k=1 to n) k^5*(n choose k). +0
3
1, 34, 342, 2192, 11000, 47232, 181888, 646144, 2156544, 6848000, 20877824, 61526016, 176171008, 492126208, 1345536000, 3610247168, 9526771712, 24769069056, 63546720256, 161087488000, 403925630976, 1002841309184 (list; graph; listen)
OFFSET

1,2

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).

LINKS

Harry J. Smith, Table of n, a(n) for n=1,...,200

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)

MAPLE

with(combinat): for n from 1 to 70 do printf(`%d, `, sum(k^5*binomial(n, k), k=1..n)) od:

PROGRAM

(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]

CROSSREFS

Sequence in context: A160146 A101092 A034978 this_sequence A135243 A033914 A159655

Adjacent sequences: A059335 A059336 A059337 this_sequence A059339 A059340 A059341

KEYWORD

nonn,easy

AUTHOR

Pat Costello (matcostello(AT)acs.eku.edu), Jan 26 2001

EXTENSIONS

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 29 2001

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Last modified November 25 08:46 EST 2009. Contains 167481 sequences.


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