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A086755
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Sum_{k=1..n} (k(k+1))^2/2.
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0
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2, 20, 92, 292, 742, 1624, 3192, 5784, 9834, 15884, 24596, 36764, 53326, 75376, 104176, 141168, 187986, 246468, 318668, 406868, 513590, 641608, 793960, 973960, 1185210, 1431612, 1717380, 2047052, 2425502, 2857952, 3349984, 3907552
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OFFSET
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0,1
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LINKS
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FORMULA
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(n+1)(n+2)(n+3)(3n^2+12n+10)/30 = 2*A024166(n+1).
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EXAMPLE
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a(3)=(1*2)^2/2+(2*3)^2/2+(3.4)^2/2=2+18+72=92
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MATHEMATICA
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Table[Sum[(k(k+1))^2/2, {k, n}], {n, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {2, 20, 92, 292, 742, 1624}, 40] (* Harvey P. Dale, Oct 04 2020 *)
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PROG
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(PARI) for(i=1, 20, print1(", "sum(j=1, i, (j*(j+1))^2/2)))
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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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STATUS
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approved
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