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A089669
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Let S3 := (n,t)->add( k^t * (add( binomial(n,j), j=0..k))^3, k=0..n); a(n) = S3(n,1).
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0
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0, 8, 155, 2286, 29296, 344140, 3807774, 40327280, 413058080, 4120742808, 40242188170, 386141947972, 3650905945872, 34087726136672, 314844824466704, 2880757518523200, 26141327872575616, 235490128979282224, 2107598857648209954, 18752794473550896332
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