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A346292
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a(0) = 1; a(n) = (1/n) * Sum_{k=3..n} (binomial(n,k) * k!)^2 * a(n-k) / k.
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1
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1, 0, 0, 4, 36, 576, 17600, 694800, 35802144, 2391438336, 200018045952, 20476348214400, 2521840589347200, 368057828019898368, 62841061478699292672, 12413136137144581203456, 2809529229255558769612800, 722458985698006017844838400, 209487621780682072569567903744
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OFFSET
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0,4
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LINKS
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FORMULA
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Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( polylog(2,x) - x - x^2 / 4 ).
Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( Sum_{n>=3} x^n / n^2 ).
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MATHEMATICA
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a[0] = 1; a[n_] := a[n] = (1/n) Sum[(Binomial[n, k] k!)^2 a[n - k]/k, {k, 3, n}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[PolyLog[2, x] - x - x^2/4], {x, 0, nmax}], x] Range[0, nmax]!^2
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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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