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A016829
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a(n) = (4n+2)^5.
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1
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32, 7776, 100000, 537824, 1889568, 5153632, 11881376, 24300000, 45435424, 79235168, 130691232, 205962976, 312500000, 459165024, 656356768, 916132832, 1252332576, 1680700000, 2219006624, 2887174368, 3707398432, 4704270176, 5904900000, 7339040224, 9039207968, 11040808032
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OFFSET
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0,1
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LINKS
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FORMULA
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a(0)=32, a(1)=7776, a(2)=100000, a(3)=537824, a(4)=1889568, a(5)=5153632, a(n)=6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)- a(n-6).
G.f.: (32*(x+1)*(x*(x*(x*(x+236)+1446)+236)+1))/(x-1)^6. (End)
Sum_{n>=0} 1/a(n) = 31*zeta(5)/1024.
Sum_{n>=0} (-1)^n/a(n) = 5*Pi^5/49152. (End)
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MATHEMATICA
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(4Range[0, 20]+2)^5 (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {32, 7776, 100000, 537824, 1889568, 5153632}, 20] (* Harvey P. Dale, Aug 31 2011 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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