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 A092043 Numerator of n!/n^2. 5
 1, 1, 2, 3, 24, 20, 720, 630, 4480, 36288, 3628800, 3326400, 479001600, 444787200, 5811886080, 81729648000, 20922789888000, 19760412672000, 6402373705728000, 6082255020441600, 115852476579840000, 2322315553259520000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Numerator of expansion of dilog(x) = Li_2(x) = - int(0, x, log(1-t)/t*dt). See the Weisstein link. E.g.f. of {a(n)/A014973(n)}_{n>=1} is Li_2(x) (with 0 for n=0). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 A. N. Kirillov, Dilogarithm identities, arXiv:hep-th/9408113, 1994. Eric Weisstein's World of Mathematics, Dilogarithm FORMULA From Wolfdieter Lang, Apr 28 2017: (Start) a(n) = numerator(n!/n^2) = numerator((n-1)!/n), n >= 1. See the name. E.g.f. {a(n)/A014973(n)}_{n>=1} with 0 for n=0 is  Li_2(x). See the comment. (-1)^n*a(n+1)/A014973(n+1) = (-1)^n*n!/(n+1) = Sum_{k=0..n} Stirling1(n, k)*Bernoulli(k), with Stirling1 = A048994 and Bernoulli(k) = A027641(k)/A027642(k), n >= 0. From inverting the formula for B(k) in terms of Stirling2 = A048993.(End) MATHEMATICA Table[Numerator[n!/n^2], {n, 1, 40}] (* Vincenzo Librandi, Apr 15 2014 *) Table[(n-1)!/n, {n, 30}]//Numerator (* Harvey P. Dale, Apr 03 2018 *) PROG (PARI) a(n)=numerator(n!/n^2) (PARI) a(n)=numerator(polcoeff(serlaplace(dilog(x)), n)) (MAGMA) [Numerator(Factorial(n)/n^2): n in [1..30]]; // Vincenzo Librandi, Apr 15 2014 CROSSREFS Denominator is in A014973. Cf. A001819. Sequence in context: A170909 A160606 A099617 * A055067 A037319 A032811 Adjacent sequences:  A092040 A092041 A092042 * A092044 A092045 A092046 KEYWORD nonn,easy,frac AUTHOR Ralf Stephan, Mar 28 2004 EXTENSIONS Comment rewritten by Wolfdieter Lang, Apr 28 2017 STATUS approved

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Last modified January 20 15:21 EST 2021. Contains 340302 sequences. (Running on oeis4.)