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%I A209923 #5 Mar 30 2012 18:37:38
%S A209923 1,1,4,26,237,2778,39805,674125,13174189,291802238,7223963796,
%T A209923 197670359937,5924155984714,192988681624915,6789966027406003,
%U A209923 256591956638230811,10365414610788266136,445744854494435066418,20330276980162447348231,980249560154126513379574
%N A209923 E.g.f. A(x) satisfies: A( x - x^2/2 - Sum_{n>=3} (n-3)!*x^n/n! ) = x.
%C A209923 Compare e.g.f. to the identity: let W(x) = Sum_{n>=1} (n-1)^(n-1)*x^n/n!, then W( x - Sum_{n>=1} x^(n+1)/(n*(n+1)) ) = x.
%e A209923 E.g.f.: A(x) = x + x^2/2! + 4*x^3/3! + 26*x^4/4! + 237*x^5/5! +...
%e A209923 Let R(x) be the series reversion of e.g.f. A(x), then R(x) begins:
%e A209923 R(x) = x - x^2/(1*2) - x^3/(1*2*3) - x^4/(2*3*4) - x^5/(3*4*5) - x^6/(4*5*6) -...
%o A209923 (PARI) {a(n)=n!*polcoeff(serreverse(x-x^2/2-sum(m=3,n,(m-3)!*x^m/m!) +x*O(x^n)),n)}
%o A209923 for(n=1,25,print1(a(n),", "))
%K A209923 nonn
%O A209923 1,3
%A A209923 _Paul D. Hanna_, Mar 15 2012

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