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A069076
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a(n) = (4*n^2 - 1)^3.
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1
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27, 3375, 42875, 250047, 970299, 2924207, 7414875, 16581375, 33698267, 63521199, 112678587, 190109375, 307546875, 480048687, 726572699, 1070599167, 1540798875, 2171747375, 3004685307, 4088324799, 5479701947, 7245075375
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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Konrad Knopp, Theory and application of infinite series, Dover, p. 269.
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = (32 - 3*Pi^3)/64.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7); a(1)=27, a(2)=3375, a(3)=42875, a(4)=250047, a(5)=970299, a(6)=2924207, a(7)=7414875. - Harvey P. Dale, Jan 20 2012
G.f: x*(x^6 - 34*x^5 - 3165*x^4 - 19852*x^3 - 19817*x^2 - 3186*x - 27)/(x-1)^7. - Harvey P. Dale, Jan 20 2012
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^3/128 + 3*Pi/32 - 1/2. - Amiram Eldar, Feb 25 2022
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MATHEMATICA
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(4Range[30]^2-1)^3 (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {27, 3375, 42875, 250047, 970299, 2924207, 7414875}, 30] (* Harvey P. Dale, Jan 20 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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STATUS
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approved
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