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A354942
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a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * (-3)^(n-k).
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2
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1, -2, -13, 60, 1113, 1002, -149049, -1932696, 7188705, 676972566, 10821753819, -32865363468, -5892948042327, -144308265498270, -748826955982593, 74472859430936928, 3199088479682040129, 57854159449349840046, -654712764990637945725, -87482030500940669619156
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OFFSET
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0,2
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LINKS
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FORMULA
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Sum_{n>=0} a(n) * x^n / n!^3 = BesselI(0,2*sqrt(x)) * Sum_{n>=0} (-3)^n * x^n / n!^3.
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MATHEMATICA
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Table[Sum[Binomial[n, k]^3 k! (-3)^(n - k), {k, 0, n}], {n, 0, 19}]
nmax = 19; CoefficientList[Series[BesselI[0, 2 Sqrt[x]] Sum[(-3)^k x^k/k!^3, {k, 0, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^3
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PROG
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(PARI) a(n) = sum(k=0, n, binomial(n, k)^3 * k! * (-3)^(n-k)); \\ Michel Marcus, Jun 12 2022
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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