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A136038
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a(n) = n^6 - n^4.
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1
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0, 0, 48, 648, 3840, 15000, 45360, 115248, 258048, 524880, 990000, 1756920, 2965248, 4798248, 7491120, 11340000, 16711680, 24054048, 33907248, 46915560, 63840000, 85571640, 113145648, 147756048, 190771200, 243750000, 308458800, 386889048, 481275648
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OFFSET
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0,3
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LINKS
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FORMULA
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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).
G.f.: 24*x^2*(1+x)*(2*x^2+11*x+2)/(1-x)^7. (End)
Sum_{n>=2} 1/a(n) = 11/4 - Pi^2/6 - Pi^4/90 = 11/4 - A013661 - A013662.
Sum_{n>=2} (-1)^n/a(n) = 7*Pi^4/720 + Pi^2/12 - 7/4 = A267315 + A072691 - 7/4. (End)
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MAPLE
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MATHEMATICA
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LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 48, 648, 3840, 15000, 45360}, 30] (* Harvey P. Dale, May 17 2018 *)
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PROG
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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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