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

1, 1, 3, 13, 87, 881, 13983, 358401, 15066943, 1031686513, 113292940383, 19641727327289, 5313784519456383, 2223596389445643993, 1429685952797008548463, 1404762001155914382481537, 2099828629077697954958843007

Offset: 0

Author

Paul D. Hanna, Oct 03 2011

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 87*x^4/4! + 881*x^5/5! +...
where
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! +...
Related expansions begin:
A(2*x)^(1/2) = 1 + x + 5*x^2/2! + 37*x^3/3! + 473*x^4/4! + 9881*x^5/5! +...
A(3*x)^(1/3) = 1 + x + 7*x^2/2! + 73*x^3/3! + 1387*x^4/4! + 44341*x^5/5! +...
A(4*x)^(1/4) = 1 + x + 9*x^2/2! + 121*x^3/3! + 3057*x^4/4! + 131921*x^5/5! +...
A(5*x)^(1/5) = 1 + x + 11*x^2/2! + 181*x^3/3! + 5711*x^4/4! + 310601*x^5/5! +...
A(6*x)^(1/6) = 1 + x + 13*x^2/2! + 253*x^3/3! + 9577*x^4/4! + 628681*x^5/5! +...
		

Crossrefs

Cf. A125281.

Programs

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)}