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A209923 E.g.f. A(x) satisfies: A( x - x^2/2 - Sum_{n>=3} (n-3)!*x^n/n! ) = x. 1

%I

%S 1,1,4,26,237,2778,39805,674125,13174189,291802238,7223963796,

%T 197670359937,5924155984714,192988681624915,6789966027406003,

%U 256591956638230811,10365414610788266136,445744854494435066418,20330276980162447348231,980249560154126513379574

%N E.g.f. A(x) satisfies: A( x - x^2/2 - Sum_{n>=3} (n-3)!*x^n/n! ) = x.

%C 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 E.g.f.: A(x) = x + x^2/2! + 4*x^3/3! + 26*x^4/4! + 237*x^5/5! +...

%e Let R(x) be the series reversion of e.g.f. A(x), then R(x) begins:

%e 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 (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 for(n=1,25,print1(a(n),", "))

%K nonn

%O 1,3

%A _Paul D. Hanna_, Mar 15 2012

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Last modified April 19 18:50 EDT 2019. Contains 322290 sequences. (Running on oeis4.)