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A336291
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a(n) = (n!)^2 * Sum_{k=1..n} 1 / (k * ((n-k)!)^2).
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2
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0, 1, 6, 39, 424, 7905, 227766, 9324511, 512970144, 36452217969, 3247711402870, 354391640998791, 46474986465907176, 7210874466760191409, 1306387103147257800774, 273269900360634449732895, 65363179181419926246184576, 17726298367452515070739268001
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OFFSET
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0,3
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LINKS
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FORMULA
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Sum_{n>=0} a(n) * x^n / (n!)^2 = -log(1 - x) * BesselI(0,2*sqrt(x)).
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MATHEMATICA
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Table[(n!)^2 Sum[1/(k ((n - k)!)^2), {k, 1, n}], {n, 0, 17}]
nmax = 17; CoefficientList[Series[-Log[1 - x] BesselI[0, 2 Sqrt[x]], {x, 0, nmax}], x] Range[0, nmax]!^2
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PROG
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(PARI) a(n) = (n!)^2 * sum(k=1, n, 1 / (k * ((n-k)!)^2)); \\ Michel Marcus, Jul 17 2020
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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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