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A280780
Numerators of coefficients in asymptotic expansion of S_n (number of simple permutations, A111111).
7
1, -4, 2, -40, -182, -7624, -202652, -14115088, -30800534, -16435427656, -1051314228316, -22675483971248, -6980651581556876, -283099764343781072, -163910651754113166328, -43009695328217994139936, -793529010007812171331166, -20144221762701827321778088, -274475989492312981198559876
OFFSET
0,2
LINKS
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
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Jan 19 2017
EXTENSIONS
More terms from Gheorghe Coserea, Jan 22 2017
STATUS
approved