A088189 Expansion of e.g.f.: 1/(1-sinh(x)-x-x^2).
1, 2, 10, 73, 712, 8681, 127004, 2167789, 42287088, 928006801, 22628305012, 606939739253, 17759375280200, 562952693773081, 19217673118604172, 702899000556953437, 27422924828816762848, 1136746326170994466337, 49892691063347466789860, 2311486678172789188448965, 112725522031113629713962552
Offset: 0
Keywords
Programs
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Mathematica
CoefficientList[Series[1/(1-Sinh[x]-x-x^2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)
Formula
a(n) ~ n!/((cosh(r)+1+2*r)*r^(n+1)), where r = 0.41010884430143... is the root of the equation r+r^2+sinh(r)=1. - Vaclav Kotesovec, Jun 27 2013
Extensions
a(0) = 1 prepended by Georg Fischer, Apr 25 2025