A234303 - OEIS

%I #3 Dec 22 2013 19:27:37

%S 1,1,3,21,243,4033,88579,2448797,82364899,3289214713,153124779251,

%T 8192660285429,498079027659539,34090100961715761,2606369415952417187,

%U 221123234953585638989,20697146958115491545091,2126375962641919801375721,238685649016900987418110355,29151156993731776756459644837

%N  E.g.f. satisfies: A(x) = Sum_{n>=0} Product_{k=1..n} Integral A(x)^(2*k-1) dx.

%e  E.g.f.: A(x) = 1 + x + 3*x^2/2! + 21*x^3/3! + 243*x^4/4! + 4033*x^5/5! +...

%e where

%e A(x) = 1 + [Integral A(x) dx] + [Integral A(x) dx]*[Integral A(x)^3 dx] + [Integral A(x) dx]*[Integral A(x)^3 dx]*[Integral A(x)^5 dx] +...

%e Related series:

%e A(x)^3 = 1 + 3*x + 15*x^2/2! + 123*x^3/3! + 1503*x^4/4! + 25239*x^5/5! +...

%e A(x)^5 = 1 + 5*x + 35*x^2/2! + 345*x^3/3! + 4635*x^4/4! + 81485*x^5/5! +...

%e A(x)^7 = 1 + 7*x + 63*x^2/2! + 735*x^3/3! + 10983*x^4/4! + 205891*x^5/5! +...

%e A(x)^9 = 1 + 9*x + 99*x^2/2! + 1341*x^3/3! + 22275*x^4/4! + 448857*x^5/5! +...

%o  (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1,n,prod(k=1,m,intformal(A^(2*k-1)+x*O(x^n))))); n!*polcoeff(A, n)}

%o for(n=0, 25, print1(a(n), ", "))

%Y  Cf. A234302.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 22 2013