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%I #3 Jul 01 2015 00:05:43
%S 1,1,5,41,438,5564,80237,1278297,22108374,410124999,8089569676,
%T 168555880750,3691281132962,84623035267642,2024303994864497,
%U 50394612947711173,1302706707186206332,34901118404682549804,967494986526757083191,27710705833750559374772,818986747695251513692537
%N G.f. A(x) satisfies: A'(x)/2 = Series_Reversion( x - x^2*A'(x) - 2*x*A(x) ).
%F a(n) = A259608(n)/n for n>=1.
%e G.f.: A(x) = x^2 + x^4 + 5*x^6 + 41*x^8 + 438*x^10 + 5564*x^12 + 80237*x^14 +...
%e where
%e A'(x)/2 = x + 2*x^3 + 15*x^5 + 164*x^7 + 2190*x^9 + 33384*x^11 + 561659*x^13 + 10226376*x^15 +...+ A259608(n)*x^(2*n-1) +...
%o (PARI) {a(n)=local(A=x); for(i=0, n, A = serreverse(x - x^2*A - x*intformal(2*A) +x*O(x^(2*n)))); polcoeff(A, 2*n-1)/n}
%o for(n=1, 25, print1(a(n), ", "))
%Y Cf. A259608.
%K nonn
%O 2,3
%A _Paul D. Hanna_, Jul 01 2015