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A019584
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a(n) = n^2*(n-1)^3/4.
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4
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0, 0, 1, 18, 108, 400, 1125, 2646, 5488, 10368, 18225, 30250, 47916, 73008, 107653, 154350, 216000, 295936, 397953, 526338, 685900, 882000, 1120581, 1408198, 1752048, 2160000, 2640625, 3203226, 3857868, 4615408, 5487525, 6486750, 7626496, 8921088, 10385793
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: x^2*(1 + 12*x + 15*x^2 + 2*x^3)/(1 - x)^6. - Colin Barker, May 04 2012
a(n) = Sum_{i=0..n-1} (n-1)*(n-1-i)^3 for n>0. - Bruno Berselli, Oct 31 2017
Sum_{n>=2} 1/a(n) = 16 - 2*Pi^2 + 4*zeta(3).
Sum_{n>=2} (-1)^n/a(n) = 24*log(2) - 16 - Pi^2/3 + 3*zeta(3). (End)
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MATHEMATICA
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Table[n^2*(n-1)^3/4, {n, 0, 100}]
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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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