A089963 a(n) = Taylor coefficient at x=li(e) of the inverse of the function li(x) (the logarithm integral) multiplied by exp(n).

1, 0, -1, 2, 1, -26, 99, 90, -3627, 21054, 21735, -1465278, 11769033, 10145862, -1292734485, 13592476842, 5651236989, -2114795158962, 28081762413807, -8040489684078, -5763467251713423, 94263221264053590, -115569462262872717, -24259606258553011206, 479901663461939425317

Offset: 1

Author

Diego Dominici (dominicd(AT)newpaltz.edu), Jan 12 2004

Keywords

• sign

Comments

Define the inverse of li(x) by H(z) and the point Zo = li(e). Then H(z)= e + a(1)*exp(-1)*(z-Zo)/1 + a(2)*exp(-2)*(z-Zo)^2/2! + a(3)*exp(-3)*(z-Zo)^3/3! + ...

References

• D. Dominici, Nested derivatives: a simple method for computing series expansions of inverse functions, IJMMS 2003:58, 3699-3715.