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A104672
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a(n) = C(n+4,4)*C(n+9,n+0).
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0
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1, 50, 825, 7700, 50050, 252252, 1051050, 3775200, 12033450, 34763300, 92470378, 229265400, 534952600, 1183859600, 2500601400, 5067885504, 9898213875, 18700431750, 34284124875, 61160599500, 106419443130, 180985447500, 301393121250, 492256440000, 789661372500
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
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FORMULA
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Sum_{n>=0} 1/a(n) = 990*Pi^2 - 38297957/3920.
Sum_{n>=0} (-1)^n/a(n) = 15*Pi^2 - 12288*log(2)/7 + 4193253/3920. (End)
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EXAMPLE
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If n=0 then C(0+4,4)*C(0+9,0+0)= C(4,4)*C(9,0)=1*1=1
If n=6 then C(6+4,4)*C(6+9,6+0)= C(10,4)*C(15,6)=210*5005=1051050
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MATHEMATICA
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Table[Binomial[n+4, 4]Binomial[n+9, n], {n, 0, 20}] (* Harvey P. Dale, Nov 15 2018 *)
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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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