A193208 G.f. satisfies: A(A(x)) = Sum_{n>=1} a(n)*x^n / Product_{k=1..n} (1 - k*x), where g.f. A(x) = Sum_{n>=1} a(n)*x^n.

1, 1, 2, 9, 80, 1209, 27737, 894103, 38403519, 2115673941, 145255332677, 12151475985497, 1216265051303224, 143479123196637632, 19697155685049948369, 3112917525687211858754, 561063341027596872760709, 114388074212705591785616006

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Example

 G.f.: A(x) = x + x^2 + 2*x^3 + 9*x^4 + 80*x^5 + 1209*x^6 + 27737*x^7 +...
where
A(A(x)) = x/(1-x) + x^2/((1-x)*(1-2*x)) + 2*x^3/((1-x)*(1-2*x)*(1-3*x)) + 9*x^4/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)) + 80*x^5/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)) +...
Explicitly,
A(A(x)) = x + 2*x^2 + 6*x^3 + 29*x^4 + 236*x^5 + 3206*x^6 + 68142*x^7 +...

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/prod(k=1, m, 1-k*x +x*O(x^#A)) );
A[#A]=Vec(G)[#A]-Vec(subst(F, x, F))[#A]); if(n<1, 0, A[n])}

Crossrefs

Cf. A193207.

Sequence in context: A221460 A122720 A109519 * A279055 A320946 A135868

Adjacent sequences: A193205 A193206 A193207 * A193209 A193210 A193211

Keyword

nonn

Author

Paul D. Hanna, Jul 19 2011

Status

approved