A193210 G.f. satisfies: A(A(x)) = Sum_{n>=1} a(n)*x^n / (1 - n*x)^n, where g.f. A(x) = Sum_{n>=1} a(n)*x^n.

1, 1, 3, 24, 393, 11043, 473041, 28601334, 2315263942, 241478700774, 31517159612387, 5030510468876181, 963773726037574349, 218238081089074417113, 57654070089428439591645, 17573072391553388287162662, 6120849041684563565434585529

Offset

1,3

Links

Table of n, a(n) for n=1..17.

Example

 G.f.: A(x) = x + x^2 + 3*x^3 + 24*x^4 + 393*x^5 + 11043*x^6 +...
where
A(A(x)) = x/(1-x) + x^2/(1-2*x)^2 + 3*x^3/(1-3*x)^3 + 24*x^4/(1-4*x)^4 + 393*x^5/(1-5*x)^5 + 11043*x^6/(1-6*x)^6 +...+ a(n)*x^n/(1-n*x)^n +...
Explicitly,
A(A(x)) = x + 2*x^2 + 8*x^3 + 64*x^4 + 972*x^5 + 25599*x^6 +...

Prog

 (PARI) {a(n)=local(A=[1], F=x, G=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A);
G=sum(m=1, #A-1, A[m]*x^m/(1-m*x +x*O(x^#A))^m );
A[#A]=Vec(G)[#A]-Vec(subst(F, x, F))[#A]); if(n<1, 0, A[n])}

Crossrefs

Cf. A193209.

Sequence in context: A332975 A010791 A145169 * A065761 A002832 A233151

Adjacent sequences: A193207 A193208 A193209 * A193211 A193212 A193213

Keyword

nonn

Author

Paul D. Hanna, Jul 19 2011

Status

approved