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A105942
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a(n) = C(n+6,n)*C(n+9,6).
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0
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84, 1470, 12936, 77616, 360360, 1387386, 4624620, 13741728, 37165128, 92912820, 217273056, 479693760, 1007356896, 2024399916, 3912705720, 7303717344, 13213962300, 23241027810, 39841761960, 66720654000, 109363854600, 175763337750, 277386503940, 430459323840
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OFFSET
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0,1
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
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FORMULA
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G.f.: -((42*(x+1)*(x*(2*x+7)+2))/(x-1)^13). - Harvey P. Dale, Sep 14 2012
a(0)=84, a(1)=1470, a(2)=12936, a(3)=77616, a(4)=360360, a(5)=1387386, a(6)=4624620, a(7)=13741728, a(8)=37165128, a(9)=92912820, a(10)=217273056, a(11)=479693760, a(12)=1007356896, a(n)=13*a(n-1)- 78*a(n-2)+286*a(n-3)-715*a(n-4)+1287*a(n-5)-1716*a(n-6)+1716*a(n-7)- 1287*a(n-8)+715*a(n-9)-286*a(n-10)+78*a(n-11)-13*a(n-12)+a(n-13). - Harvey P. Dale, Sep 14 2012
Sum_{n>=0} 1/a(n) = 10446039/3920 - 270*Pi^2.
Sum_{n>=0} (-1)^n/a(n) = 82911/560 - 15*Pi^2. (End)
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EXAMPLE
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If n=0 then C(0+6,0)*C(0+9,6) = C(6,0)*C(9,6) = 1*84 = 84.
If n=6 then C(6+6,6)*C(6+9,6) = C(12,6)*C(15,6) = 924*5005 = 4624620.
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MATHEMATICA
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Table[Binomial[n+6, n]Binomial[n+9, 6], {n, 0, 30}] (* or *) CoefficientList[ Series[-((42 (x+1) (x (2 x+7)+2))/(x-1)^13), {x, 0, 30}], x] (* Harvey P. Dale, Sep 14 2012 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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