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%I A199670 #12 Oct 24 2024 03:50:27
%S A199670 1,1,3,16,119,1134,13201,181594,2882061,51836302,1041959555,
%T A199670 23148374886,563234624575,14895783741202,425457081218169,
%U A199670 13052033357204842,428016906877603589,14941465218939490686,553193807213161191259,21651761774465075118502,893244763931287659927399
%N A199670 E.g.f.: d/dx Series_Reversion( Sum_{n>=0} (-x)^(3*n)/(3*n)! - exp(-x) ).
%C A199670 Compare to e.g.f. F(x) of A183611, which satisfies F'(x) = F(x)^2 + x*F(x)^3, where F(x) = d/dx Series_Reversion( Sum_{n>=1} x^(3*n-2)/(3*n-2)! - x^(3*n-1)/(3*n-1)! ).
%e A199670 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 119*x^4/4! + 1134*x^5/5! +...
%e A199670 E.g.f.: A(x) = d/dx Series_Reversion(G(x)) where G(x) begins:
%e A199670 G(x) = x - x^2/2! - x^4/4! + x^5/5! + x^7/7! - x^8/8! - x^10/10! + x^11/11! +...
%e A199670 The series reversion of G(x) begins:
%e A199670 x + x^2/2! + 3*x^3/3! + 16*x^4/4! + 119*x^5/5! + 1134*x^6/6! +...
%o A199670 (PARI) {a(n)=n!*polcoeff(deriv(serreverse(sum(m=0, n\3+1, (-x)^(3*m)/(3*m)!)-exp(-x+x^2*O(x^n)))), n)}
%o A199670 (PARI) {a(n)=n!*polcoeff(deriv(serreverse(sum(m=1, n\3+1, -(-x)^(3*m-2)/(3*m-2)!-(-x)^(3*m-1)/(3*m-1)!+x^2*O(x^n)))), n)}
%Y A199670 Cf. A183611, A199675.
%K A199670 nonn
%O A199670 0,3
%A A199670 _Paul D. Hanna_, Nov 08 2011

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