cp's OEIS Frontend

A280780 Numerators of coefficients in asymptotic expansion of S_n (number of simple permutations, A111111).

%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, <a href="/A280780/b280780.txt">Table of n, a(n) for n = 0..100</a>
%H A280780 Michael Borinsky, <a href="https://arxiv.org/abs/1603.01236">Generating asymptotics for factorially divergent sequences</a>, 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