login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

G.f. A(x) satisfies: A'(x)/2 = Series_Reversion( x - x^2*A'(x) - 2*x*A(x) ).
1

%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