A193205 G.f. satisfies: A(A(x)) = Sum_{n>=1} a(n)*x^n * (Sum_{k=0..n} C(n,k)^2*x^k), where g.f. A(x) = Sum_{n>=1} a(n)*x^n.

1, 1, 2, 8, 76, 1452, 45612, 2095992, 131601136, 10790109464, 1117867502280, 142679360514256, 21987281765799840, 4023859534010994768, 862536439626951197192, 214034590216271750690880, 60867125826968771742513120, 19663683837171331703090010864

Offset

1,3

Links

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

Example

G.f.: A(x) = x + x^2 + 2*x^3 + 8*x^4 + 76*x^5 + 1452*x^6 + 45612*x^7 +...
where
A(A(x)) = x*(1+x) + x^2*(1+4*x+x^2) + 2*x^3*(1+9*x+9*x^2+x^3) + 8*x^4*(1+16*x+36*x^2+16*x^3+x^4) + 76*x^5*(1+25*x+100*x^2+100*x^3+25*x^4+x^5) +...
Explicitly,
A(A(x)) = x + 2*x^2 + 6*x^3 + 27*x^4 + 222*x^5 + 3642*x^6 + 105612*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*sum(k=0, m, binomial(m, k)^2*x^k) +x*O(x^#A));
A[#A]=Vec(G)[#A]-Vec(subst(F, x, F))[#A]); if(n<1, 0, A[n])}

Crossrefs

Cf. A193206.

Sequence in context: A132039 A204552 A002668 * A303943 A295345 A329968

Adjacent sequences: A193202 A193203 A193204 * A193206 A193207 A193208

Keyword

nonn

Author

Paul D. Hanna, Jul 19 2011

Status

approved