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A140354
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Binomial(n+9,9)*2^n.
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10
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1, 20, 220, 1760, 11440, 64064, 320320, 1464320, 6223360, 24893440, 94595072, 343982080, 1203937280, 4074864640, 13388840960, 42844291072, 133888409600, 409541017600, 1228623052800, 3621204787200, 10501493882880, 30004268236800
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OFFSET
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0,2
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COMMENTS
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With a different offset, number of n-permutations (n>=9) of 3 objects: u, v, z with repetition allowed, containing exactly nine (9) u's.
If n=9 then a(0)= 1
Example: a(1)=20 because we have
uuuuuuuuuv, uuuuuuuuvu, uuuuuuuvuu, uuuuuuvuuu, uuuuuvuuuu, uuuuvuuuuu, uuuvuuuuuu, uuvuuuuuuu, uvuuuuuuuu, vuuuuuuuuu, uuuuuuuuuz, uuuuuuuuzu, uuuuuuuzuu, uuuuuuzuuu, uuuuuzuuuu, uuuuzuuuuu, uuuzuuuuuu, uuzuuuuuuu, uzuuuuuuuu and zuuuuuuuuu.
Number of 9D hypercubes in an n-dimensional hypercube. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 29 2010]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..400
M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550, 2013
Index to sequences with linear recurrences with constant coefficients, signature (20,-180,960,-3360,8064,-13440,15360,-11520,5120,-1024).
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FORMULA
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G.f.: 1/(1-2*x)^10 [From Harvey P. Dale, Jul 18 2011]
a(0)=1, a(1)=20, a(2)=220, a(3)=1760, a(4)=11440, a(5)=64064, a(6)=320320, a(7)=1464320, a(8)=6223360, a(9)=24893440, a(n)=20*a(n-1)- 180*a(n-2)+ 960*a(n-3)- 3360*a(n-4)+ 8064*a(n-5)- 13440*a(n-6)+ 15360*a(n-7)- 11520*a(n-8)+ 5120*a(n-9)- 1024*a(n-10). [Harvey P. Dale, Jul 18 2011]
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MAPLE
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seq(binomial(n+9, 9)*2^n, n=0..23);
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MATHEMATICA
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Table[Binomial[n + 9, 9]*2^n, {n, 0, 20}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 29 2010]
CoefficientList[Series[1/(1-2x)^10, {x, 0, 30}], x] (* Harvey P. Dale, Jul 18 2011 *)
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PROG
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(Sage) [lucas_number2(n, 2, 0)*binomial(n, 9)/512 for n in xrange(9, 31)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 10 2009]
(PARI) a(n)=binomial(n+9, 9)<<n \\ Charles R Greathouse IV, Jul 18 2011
(MAGMA) [2^n* Binomial(n+9, 9): n in [0..30]]; // Vincenzo Librandi, Oct 14 2011
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CROSSREFS
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Sequence in context: A213351 A140236 A004411 * A155673 A000833 A178261
Adjacent sequences: A140351 A140352 A140353 * A140355 A140356 A140357
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 23 2008
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STATUS
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approved
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