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 A346410 a(n) = (n!)^2 * Sum_{k=0..n-1} 1 / ((n-k) * k!)^2. 1
 0, 1, 5, 22, 152, 2001, 45097, 1527506, 71864928, 4466430513, 353828600029, 34770661312190, 4148422395161464, 590479899466175681, 98824492409739430401, 19209838771051338898234, 4291488438323868507946880, 1091819942877526843993466529, 313819508664449992611846900981 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..18. FORMULA Sum_{n>=0} a(n) * x^n / (n!)^2 = polylog(2,x) * BesselI(0,2*sqrt(x)). MATHEMATICA Table[(n!)^2 Sum[1/((n - k) k!)^2, {k, 0, n - 1}], {n, 0, 18}] nmax = 18; CoefficientList[Series[PolyLog[2, x] BesselI[0, 2 Sqrt[x]], {x, 0, nmax}], x] Range[0, nmax]!^2 CROSSREFS Cf. A002104, A006040, A066998, A193563, A336291, A346411. Sequence in context: A028561 A227918 A009638 * A121942 A006294 A239982 Adjacent sequences: A346407 A346408 A346409 * A346411 A346412 A346413 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jul 15 2021 STATUS approved

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Last modified June 8 00:26 EDT 2023. Contains 363157 sequences. (Running on oeis4.)