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 A336809 a(n) = (n!)^2 * Sum_{k=0..n} (k+1) / ((n-k)!)^2. 1
 1, 3, 21, 271, 5649, 174051, 7447573, 422836191, 30767443521, 2792343036259, 309252314731701, 41051709426337743, 6434479982900111761, 1175819833620882461571, 247785659825802622964469, 59649892258930263778729951, 16268290830606063971956320513 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..16. FORMULA Sum_{n>=0} a(n) * x^n / (n!)^2 = BesselI(0,2*sqrt(x)) / (1 - x)^2. MATHEMATICA Table[n!^2 Sum[(k + 1)/(n - k)!^2, {k, 0, n}], {n, 0, 16}] nmax = 16; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(1 - x)^2, {x, 0, nmax}], x] Range[0, nmax]!^2 CROSSREFS Cf. A001339, A006040. Sequence in context: A277454 A215127 A227820 * A066206 A130032 A174967 Adjacent sequences: A336806 A336807 A336808 * A336810 A336811 A336812 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 27 2021 STATUS approved

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Last modified June 3 14:25 EDT 2023. Contains 363116 sequences. (Running on oeis4.)