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A128230 Expansion of exp(x)/(1 - x - x^2/2!), where a(n) = 1 + n*a(n-1) + C(n,2)*a(n-2).

%I A128230 #10 May 24 2013 03:55:19
%S A128230 1,2,6,25,137,936,7672,73361,801705,9856342,134640146,2023140417,
%T A128230 33163934641,588936102860,11263023492372,230783643185881,
%U A128230 5044101110058737,117136294344278346,2880200768035996990
%N A128230 Expansion of exp(x)/(1 - x - x^2/2!), where a(n) = 1 + n*a(n-1) + C(n,2)*a(n-2).
%H A128230 Vincenzo Librandi, <a href="/A128230/b128230.txt">Table of n, a(n) for n = 0..200</a>
%F A128230 a(n) ~ n!*exp(sqrt(3)-1)*((1+sqrt(3))/2)^(n+1)/sqrt(3) . - _Vaclav Kotesovec_, Oct 20 2012
%e A128230 E.g.f.: exp(x)/(1 - x - x^2/2!) = 1 + 2*x + 6*x^2/2! + 25*x^3/3! + 137*x^4/4! + 936*x^5/5! + 7672*x^6/6! +... + a(n)*x^n/n! +...
%e A128230 where a(n) = 1 + n*a(n-1) + n*(n-1)*a(n-2)/2.
%t A128230 CoefficientList[Series[E^x/(1-x-x^2/2), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 20 2012 *)
%o A128230 (PARI) a(n)=n!*polcoeff(exp(x+x*O(x^n))/(1-x-x^2/2! +x*O(x^n)),n)
%Y A128230 Cf. A087214, A000629, A128231, A128232.
%K A128230 nonn
%O A128230 0,2
%A A128230 _Paul D. Hanna_, Feb 20 2007