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A336588
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Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) * BesselI(0,2*sqrt(exp(x) - 1)).
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1
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1, 2, 9, 67, 725, 10616, 200767, 4740149, 136113217, 4656324934, 186642121061, 8647446227487, 457854954921949, 27435354945248732, 1844986431192663683, 138229607701444447561, 11464234006789370705537, 1046538415206891196153834, 104623195637603009050593697
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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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a(n) = n! * Sum_{k=0..n} Stirling2(n+1,k+1) / k!.
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MATHEMATICA
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nmax = 18; CoefficientList[Series[Exp[x] BesselI[0, 2 Sqrt[Exp[x] - 1]], {x, 0, nmax}], x] Range[0, nmax]!^2
Table[n! Sum[StirlingS2[n + 1, k + 1]/k!, {k, 0, n}], {n, 0, 18}]
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PROG
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(PARI) a(n) = n! * sum(k=0, n, stirling(n+1, k+1, 2) / k!); \\ Michel Marcus, Jul 27 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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