A280781 - OEIS

%I #20 Jan 22 2017 21:28:15

%S 1,1,1,3,3,15,45,315,63,2835,14175,22275,467775,1216215,42567525,

%T 638512875,638512875,834978375,558242685,1856156927625,713906510625,

%U 17717861581875,2143861251406875,9861761756471625,147926426347074375,75472666503609375,48076088562799171875

%N Denominators of coefficients in asymptotic expansion of S_n (number of simple permutations, A111111).

%C Has the same start as A046983 but is a different sequence.

%H Gheorghe Coserea, <a href="/A280781/b280781.txt">Table of n, a(n) for n = 0..100</a>

%H 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.

%e Coefficients are 1, -4, 2, -40/3, -182/3, -7624/15, -202652/45, -14115088/315, -30800534/63, -16435427656/2835, ...

%o (PARI)

%o seq(N) = {

%o   my(f = serreverse(x*Ser(vector(N, n, n!))));

%o   Vec(x* f'/f * exp(2 + (f-x)/(x*f)));

%o };

%o apply(denominator, seq(28))  \\ _Gheorghe Coserea_, Jan 22 2017

%Y Cf. A000699, A280775, A111111, A280777, A280778, A280779, A280780.

%Y Cf. also A046983.

%K nonn,frac

%O 0,4

%A _N. J. A. Sloane_, Jan 19 2017

%E More terms from _Gheorghe Coserea_, Jan 22 2017