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A216831
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a(n) = Sum_{k=0..n} binomial(n,k)^3 * k!.
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5
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1, 2, 11, 88, 905, 11246, 162607, 2668436, 48830273, 983353690, 21570885011, 511212091952, 13001401709881, 352856328962918, 10170853073795975, 310093415465876716, 9964607161173899777, 336439048405066012466, 11902368222382731461083, 440122520333417057761160
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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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Recurrence: (8*n^2+31*n+21)*a(n+3) - (24*n^3+157*n^2+308*n+162)*a(n+2) + (24*n^4+117*n^3+178*n^2+71*n-18)*a(n+1) - (8*n^2+31*n+30)*(n+1)^3*a(n) = 0.
a(n) ~ n^(n-1/6)/(sqrt(6*Pi)*exp(n+n^(1/3)-3*n^(2/3)-1/3)). - Vaclav Kotesovec, Sep 30 2012
Sum_{n>=0} a(n) * x^n / n!^3 = BesselI(0,2*sqrt(x)) * Sum_{n>=0} x^n / n!^3. - Ilya Gutkovskiy, Jun 19 2022
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MATHEMATICA
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Table[Sum[Binomial[n, k]^3*k!, {k, 0, n}], {n, 0, 25}]
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PROG
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(PARI) a(n) = sum(k=0, n, binomial(n, k)^3 * k!); \\ Michel Marcus, May 04 2021
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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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