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A256019
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a(n) = Sum_{i=1..n-1} (i^3 * a(i)), a(1)=1.
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2
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1, 1, 9, 252, 16380, 2063880, 447861960, 154064514240, 79035095805120, 57695619937737600, 57753315557675337600, 76927416322823549683200, 133007502822161917402252800, 292350491203111894450151654400, 802502098352542150265666291328000
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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Product_{i=2..n-1} (i^3 + 1), for n>2.
a(n) ~ cosh(sqrt(3)*Pi/2) / (2*Pi) * ((n-1)!)^3.
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MATHEMATICA
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Clear[a]; a[1]=1; a[n_]:= a[n] = Sum[i^3*a[i], {i, 1, n-1}]; Table[a[n], {n, 1, 20}]
Flatten[{1, Table[FullSimplify[Cosh[Sqrt[3]*Pi/2] * Gamma[n+1] * Gamma[n-1/2 - I*Sqrt[3]/2] * Gamma[n-1/2 + I*Sqrt[3]/2] / (2*Pi)], {n, 2, 20}]}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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