# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a280780 Showing 1-1 of 1 %I A280780 #26 Jan 25 2017 12:39:14 %S A280780 1,-4,2,-40,-182,-7624,-202652,-14115088,-30800534,-16435427656, %T A280780 -1051314228316,-22675483971248,-6980651581556876,-283099764343781072, %U A280780 -163910651754113166328,-43009695328217994139936,-793529010007812171331166,-20144221762701827321778088,-274475989492312981198559876 %N A280780 Numerators of coefficients in asymptotic expansion of S_n (number of simple permutations, A111111). %H A280780 Gheorghe Coserea, Table of n, a(n) for n = 0..100 %H A280780 Michael Borinsky, Generating asymptotics for factorially divergent sequences, arXiv preprint arXiv:1603.01236 [math.CO], 2016. %F A280780 A111111(n) ~ n!*exp(-2)*(1 - 4/n + 2/(n*(n-1)) - (40/3)/(n*(n-1)*(n-2)) - ...). - _Gheorghe Coserea_, Jan 23 2017 %e A280780 Coefficients are 1, -4, 2, -40/3, -182/3, -7624/15, -202652/45, -14115088/315, -30800534/63, -16435427656/2835, ... %o A280780 (PARI) %o A280780 seq(N) = { %o A280780 my(f = serreverse(x*Ser(vector(N, n, n!)))); %o A280780 Vec(x* f'/f * exp(2 + (f-x)/(x*f))); %o A280780 }; %o A280780 apply(numerator, seq(20)) \\ _Gheorghe Coserea_, Jan 22 2017 %Y A280780 Cf. A000699, A280775, A111111, A280777, A280778, A280779, A280781. %K A280780 sign,frac %O A280780 0,2 %A A280780 _N. J. A. Sloane_, Jan 19 2017 %E A280780 More terms from _Gheorghe Coserea_, Jan 22 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE