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%I #9 Nov 06 2019 01:10:34
%S 1,-12,3472,-20044992,-47937777408,-20305698249280512,
%T -2854719816291959009280,-1250271985277826533770444800,
%U -852308886538376231161133484933120,-1020041468410487908146642041792342261760,-1902990477565541776130152995745141108333608960
%N Expansion of e.g.f. sech(arcsinh(x)*arcsin(x)) in powers of x^4.
%H Andrew Howroyd, <a href="/A012609/b012609.txt">Table of n, a(n) for n = 0..50</a>
%e 1 - 12/4!*x^4 + 3472/8!*x^8 - 20044992/12!*x^12 ...
%o (PARI) a(n)={my(x=x+O(x*x^(4*n))); polcoef(serlaplace(1/cosh(asinh(x)*asin(x))), 4*n)} \\ _Andrew Howroyd_, Nov 05 2019
%K sign
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Terms a(8) and beyond from _Andrew Howroyd_, Nov 05 2019