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%I M0676 #27 Oct 05 2022 04:58:33
%S 1,-2,3,-5,7,-14,11,-66,-127,-992,-5029,-30899,-193321,-1285300,
%T -8942561,-65113125,-494605857,-3911658640,-32145949441,-274036507173,
%U -2419502677445,-22093077575496,-208364964369913,-2027216779571754,-20323053380033763,-209715614081160850
%N Reversion of o.g.f. for Bell numbers (A000110) omitting a(0)=1.
%C As the definition says, this entry deliberately omits the zero-th term 1. - _N. J. A. Sloane_, Jun 16 2021
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} Bell(k) * A(x)^k. - _Ilya Gutkovskiy_, Apr 22 2020
%p read transforms; A := series(exp(exp(x)-1),x,60); SERIESTOLISTMULT(%); subsop(1=NULL,%); REVERT(%);
%p # Alternative, using function CompInv from A357588:
%p CompInv(26, n -> combinat:-bell(n)); # _Peter Luschny_, Oct 05 2022
%o (PARI) a(n)=if(n<1,0,polcoeff(serreverse(-1+serlaplace(exp(exp(x+x*O(x^n))-1))),n))
%Y Cf. A000110.
%K sign
%O 1,2
%A _N. J. A. Sloane_, _Mira Bernstein_
%E Signs corrected Dec 24 2001
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