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

1, -4, 2, -40, -182, -7624, -202652, -14115088, -30800534, -16435427656, -1051314228316, -22675483971248, -6980651581556876, -283099764343781072, -163910651754113166328, -43009695328217994139936, -793529010007812171331166, -20144221762701827321778088, -274475989492312981198559876

Offset

0,2

Links

Gheorghe Coserea, Table of n, a(n) for n = 0..100

Michael Borinsky, Generating asymptotics for factorially divergent sequences, arXiv preprint arXiv:1603.01236 [math.CO], 2016.

Formula

A111111(n) ~ n!*exp(-2)*(1 - 4/n + 2/(n*(n-1)) - (40/3)/(n*(n-1)*(n-2)) - ...). - Gheorghe Coserea, Jan 23 2017

Example

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

Prog

(PARI)
seq(N) = {
  my(f = serreverse(x*Ser(vector(N, n, n!))));
  Vec(x* f'/f * exp(2 + (f-x)/(x*f)));
};
apply(numerator, seq(20))  \\ Gheorghe Coserea, Jan 22 2017

Crossrefs

Cf. A000699, A280775, A111111, A280777, A280778, A280779, A280781.

Sequence in context: A307974 A303625 A123850 * A264755 A120968 A193894

Adjacent sequences: A280777 A280778 A280779 * A280781 A280782 A280783

Keyword

sign,frac

Author

N. J. A. Sloane, Jan 19 2017

Extensions

More terms from Gheorghe Coserea, Jan 22 2017

Status

approved