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A162669
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a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)/5.
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2
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0, 144, 1008, 4032, 12096, 30240, 66528, 133056, 247104, 432432, 720720, 1153152, 1782144, 2673216, 3907008, 5581440, 7814016, 10744272, 14536368, 19381824, 25502400, 33153120, 42625440, 54250560, 68402880, 85503600, 106024464, 130491648, 159489792, 193666176
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: 144*x/(1-x)^7. (End)
E.g.f.: x*(720 +1800*x +1200*x^2 +300*x^3 +30*x^4 +x^5)*exp(x)/5. - G. C. Greubel, Aug 27 2019
Sum_{n>=1} 1/a(n) = 1/120.
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/3 - 661/720. (End)
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MAPLE
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seq(144*binomial(n+5, 6), n = 0..30); # G. C. Greubel, Aug 27 2019
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MATHEMATICA
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CoefficientList[Series[144*x/(1-x)^7, {x, 0, 30}], x] (* Vincenzo Librandi, Mar 05 2012 *)
Table[(Times@@(n+Range[0, 5]))/5, {n, 0, 30}] (* Harvey P. Dale, Jul 01 2019 *)
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PROG
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(Magma) [n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)/5: n in [1..30]]; // Vincenzo Librandi, Mar 05 2012
(PARI) vector(30, n, 144*binomial(n+4, 6)) \\ G. C. Greubel, Aug 27 2019
(Sage) [144*binomial(n+5, 6) for n in (0..30)] # G. C. Greubel, Aug 27 2019
(GAP) List([0..30], n-> 144*Binomial(n+5, 6)); # G. C. Greubel, Aug 27 2019
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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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EXTENSIONS
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Definition factorized, offset corrected by R. J. Mathar, Jul 13 2009
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STATUS
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approved
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