A196562 E.g.f. satisfies: A(x) = 1 + Sum{n>=1} x^n * A(n^2*x)^(1/n) / n!.

1, 1, 3, 16, 197, 5556, 402727, 68650114, 28060721817, 25837746071608, 54301560755743691, 252957269930383300734, 2621503487300921168212357, 59671929727060536957652131604, 2977392188346587645059521680164959

Offset: 0

Author

Paul D. Hanna, Oct 03 2011

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 197*x^4/4! + 5556*x^5/5! +...
where
A(x) = 1 + x*A(x) + x^2*A(4*x)^(1/2)/2! + x^3*A(9*x)^(1/3)/3! + x^4*A(16*x)^(1/4)/4! +...
Related expansions begin:
A(4*x)^(1/2) = 1 + 2*x + 20*x^2/2! + 392*x^3/3! + 20880*x^4/4! +...
A(9*x)^(1/3) = 1 + 3*x + 63*x^2/2! + 2700*x^3/3! + 335421*x^4/4! +...
A(16*x)^(1/4) = 1 + 4*x + 144*x^2/2! + 10816*x^3/3! + 2437376*x^4/4! +...
A(25*x)^(1/5) = 1 + 5*x + 275*x^2/2! + 32000*x^3/3! + 11413125*x^4/4! +...
A(36*x)^(1/6) = 1 + 6*x + 468*x^2/2! + 77976*x^3/3! + 40405392*x^4/4! +...
		

Crossrefs

Cf. A196561, 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^2*x+x*O(x^n))^(1/m)));n!*polcoeff(A,n)}