A182957 G.f.: A(x) = x/Series_Reversion(x*G(x)) where G(x) = Sum_{n>=0} n^n*x^n.

1, 1, 3, 17, 151, 1824, 27541, 494997, 10273039, 241217147, 6314907390, 182283959604, 5750796304553, 196865960240416, 7268410972604665, 287920792767378837, 12181570018235995359, 548274960053921957856

Offset: 0

Author

Paul D. Hanna, Dec 31 2010

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 17*x^3 + 151*x^4 + 1824*x^5 +...
G.f. satisfies A(x) = G(x/A(x)) where A(x*G(x)) = G(x) begins:
G(x) = 1 + x + 2^2*x^2 + 3^3*x^3 + 4^4*x^4 + 5^5*x^5 + 6^6*x^6 +...
so that:
A(x) = 1 + x/A(x) + 2^2*x^2/A(x)^2 + 3^3*x^3/A(x)^3 + 4^4*x^4/A(x)^4 +...
The coefficients in A(x)^n for n=1..8 begin:
A^1: [(1), 1, 3, 17, 151, 1824, 27541, 494997, ...];
A^2: [1,(2), 7, 40, 345, 4052, 59925, 1061154, ...];
A^3: [1, 3,(12), 70, 591, 6762, 97938, 1707987, ...];
A^4: [1, 4, 18,(108), 899, 10044, 142488, 2446336, ...];
A^5: [1, 5, 25, 155,(1280), 14001, 194620, 3288540, ...];
A^6: [1, 6, 33, 212, 1746,(18750), 255532, 4248630, ...];
A^7: [1, 7, 42, 280, 2310, 24423,(326592), 5342541, ...];
A^8: [1, 8, 52, 360, 2986, 31168, 409356, (6588344), ...]; ...
where the coefficient of x^n in A(x)^(n+1)/(n+1) equals n^n.
		

Crossrefs

Cf. A180747, A180749.

Programs

PARI

{a(n)=polcoeff(x/serreverse(sum(m=1,n+1,(m-1)^(m-1)*x^m)+x^2*O(x^n)),n)}

Formula

G.f. satisfies: A(x) = G(x/A(x)) where A(x*G(x)) = G(x) = Sum_{n>=0} n^n*x^n.

G.f. satisfies: [x^n] A(x)^(n+1)/(n+1) = n^n.