cp's OEIS Frontend

A196561 E.g.f. satisfies: A(x) = 1 + Sum{n>=1} x^n * A(n*x)^(1/n) / n!.

%I A196561 #11 Aug 25 2024 13:36:50
%S A196561 1,1,3,13,87,881,13983,358401,15066943,1031686513,113292940383,
%T A196561 19641727327289,5313784519456383,2223596389445643993,
%U A196561 1429685952797008548463,1404762001155914382481537,2099828629077697954958843007
%N A196561 E.g.f. satisfies: A(x) = 1 + Sum{n>=1} x^n * A(n*x)^(1/n) / n!.
%e A196561 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 87*x^4/4! + 881*x^5/5! +...
%e A196561 where
%e A196561 A(x) = 1 + x*A(x) + x^2*A(2*x)^(1/2)/2! + x^3*A(3*x)^(1/3)/3! + x^4*A(4*x)^(1/4)/4! +...
%e A196561 Related expansions begin:
%e A196561 A(2*x)^(1/2) = 1 + x + 5*x^2/2! + 37*x^3/3! + 473*x^4/4! + 9881*x^5/5! +...
%e A196561 A(3*x)^(1/3) = 1 + x + 7*x^2/2! + 73*x^3/3! + 1387*x^4/4! + 44341*x^5/5! +...
%e A196561 A(4*x)^(1/4) = 1 + x + 9*x^2/2! + 121*x^3/3! + 3057*x^4/4! + 131921*x^5/5! +...
%e A196561 A(5*x)^(1/5) = 1 + x + 11*x^2/2! + 181*x^3/3! + 5711*x^4/4! + 310601*x^5/5! +...
%e A196561 A(6*x)^(1/6) = 1 + x + 13*x^2/2! + 253*x^3/3! + 9577*x^4/4! + 628681*x^5/5! +...
%o A196561 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m/m!*subst(A,x,m*x+x*O(x^n))^(1/m)));n!*polcoeff(A,n)}
%Y A196561 Cf. A125281.
%K A196561 nonn
%O A196561 0,3
%A A196561 _Paul D. Hanna_, Oct 03 2011