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 A346405 a(n) = (n!)^2 * Sum_{k=0..n-1} 1 / ((n-k)^2 * k!). 1
 0, 1, 5, 31, 268, 3476, 70656, 2202432, 98622336, 5954736384, 463100042880, 44924476970880, 5308404719823360, 749930460864929280, 124754522068412651520, 24129984694192721971200, 5368254991077002482483200, 1360938718277588430567014400, 389980903967231535140578099200 (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) * exp(x). MATHEMATICA Table[(n!)^2 Sum[1/((n - k)^2 k!), {k, 0, n - 1}], {n, 0, 18}] nmax = 18; CoefficientList[Series[PolyLog[2, x] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!^2 CROSSREFS Cf. A001819, A002104, A002720, A061573, A346409. Sequence in context: A294216 A058892 A177453 * A259787 A273601 A218679 Adjacent sequences: A346402 A346403 A346404 * A346406 A346407 A346408 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jul 15 2021 STATUS approved

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Last modified August 3 09:58 EDT 2024. Contains 374885 sequences. (Running on oeis4.)