A193207 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, 1, 2, 11, 126, 2383, 65847, 2484405, 122300214, 7600462726, 581393350442, 53649579705613, 5874521948167920, 752862908769402263, 111616832101497426539, 18952126477270139013143, 3653537196995939362232795, 793546121525181745226364532

Offset

1,4

Links

Table of n, a(n) for n=1..19.

Example

 G.f.: A(x) = x + x^2 + x^3 + 2*x^4 + 11*x^5 + 126*x^6 + 2383*x^7 +...
where
A(A(x)) = x*(1+x) + x^2*(1+x)*(1+2*x) + x^3*(1+x)*(1+2*x)*(1+3*x) + 2*x^4*(1+x)*(1+2*x)*(1+3*x)*(1+4*x) + 11*x^5*(1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x) +...
Explicitly,
A(A(x)) = x + 2*x^2 + 4*x^3 + 10*x^4 + 42*x^5 + 367*x^6 + 6064*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. A193208.

Sequence in context: A342357 A279703 A206401 * A112864 A077391 A104087

Adjacent sequences: A193204 A193205 A193206 * A193208 A193209 A193210

Keyword

nonn

Author

Paul D. Hanna, Jul 19 2011

Status

approved