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%I A277413 #7 Nov 17 2016 00:53:58
%S A277413 1,3,70,4620,599256,128648520,41281606080,18507916627200,
%T A277413 11049593741746560,8474451191616009600,8119493428719228192000,
%U A277413 9504049395027168805824000,13345312208487981260926464000,22140681034117932250214874624000,42846437958647788197412779939840000,95657301566159892238019686222356480000,244038306493164073323605513327887380480000
%N A277413 E.g.f.: Series_Reversion( x + Sum_{n>=2} (-1)^(n-1) * x^(2*n-1)/(n*(n-1)) )  =  Sum_{n>=1} a(n)*x^(2*n-1)/(2*n-1)!.
%e A277413 E.g.f.: A(x) = x + 3*x^3/3! + 70*x^5/5! + 4620*x^7/7! + 599256*x^9/9! + 128648520*x^11/11! + 41281606080*x^13/13! + 18507916627200*x^15/15! +...
%e A277413 such that
%e A277413 Series_Reversion(A(x)) = x - x^3/(1*2) + x^5/(2*3) - x^7/(3*4) + x^9/(4*5) - x^11/(5*6) + x^13/(6*7) +...+ (-1)^(n-1)*x^(2*n-1)/(n*(n-1)) +...
%o A277413 (PARI) {a(n) = (2*n-1)! * polcoeff( serreverse(x - sum(m=2,n,(-1)^m * x^(2*m-1) / (m*(m-1)) ) +O(x^(2*n+2))), 2*n-1)}
%o A277413 for(n=1,25,print1(a(n),", "))
%K A277413 nonn
%O A277413 1,2
%A A277413 _Paul D. Hanna_, Nov 17 2016

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