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A101862
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a(n) = n*(n+1)*(n+7)*(122+57*n+n^2)/120.
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2
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24, 108, 302, 671, 1296, 2275, 3724, 5778, 8592, 12342, 17226, 23465, 31304, 41013, 52888, 67252, 84456, 104880, 128934, 157059, 189728, 227447, 270756, 320230, 376480, 440154, 511938, 592557, 682776, 783401, 895280, 1019304, 1156408, 1307572, 1473822, 1656231
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OFFSET
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1,1
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COMMENTS
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6th partial summation within series as series accumulate n times from an initial sequence of Euler Triangle's row 4: 1,11,11,1: 6th row of the array in the examples of A101860.
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LINKS
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FORMULA
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G.f.: x*(2-x)*(x^2-12*x+12) / (1-x)^6. - R. J. Mathar, Dec 06 2011
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) for n > 6. - Wesley Ivan Hurt, Dec 06 2016
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MAPLE
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MATHEMATICA
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Table[n*(n + 1)*(n + 7)*(122 + 57*n + n^2)/120, {n, 50}] (* Wesley Ivan Hurt, Dec 06 2016 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {24, 108, 302, 671, 1296, 2275}, 50] (* Harvey P. Dale, Oct 15 2020 *)
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PROG
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(Magma) [n*(n + 1)*(n + 7)*(122 + 57*n + n^2)/120 : n in [1..50]]; // Wesley Ivan Hurt, Dec 06 2016
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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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Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004
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STATUS
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approved
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