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A136008
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a(n) = n^6 - n^2.
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1
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0, 0, 60, 720, 4080, 15600, 46620, 117600, 262080, 531360, 999900, 1771440, 2985840, 4826640, 7529340, 11390400, 16776960, 24137280, 34011900, 47045520, 63999600, 85765680, 113379420, 148035360, 191102400, 244140000, 308915100
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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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Sum_{n>=2} 1/a(n) = 7/8 - Pi^2/6 + Pi*coth(Pi)/4.
Sum_{n>=2} (-1)^n/a(n) = -7/8 + Pi^2/12 + Pi*csch(Pi)/4 = -7/8 + A072691 + (1/4) * A090986. (End)
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). - Wesley Ivan Hurt, May 04 2021
a(n) = 6*binomial(n^2 + 1, 3).
E.g.f.: x^2*(30 +90*x +65*x^2 +15*x^3 +x^4)*exp(x). (End)
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MATHEMATICA
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PROG
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(Magma) [6*Binomial(n^2 +1, 3): n in [0..30]]; // G. C. Greubel, Feb 07 2022
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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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