A212277 G.f. satisfies: A(x) = x + A(A(x)^2)^2 where g.f. A(x) = Sum_{n>=1} a(n)*x^(3*n-2).

1, 1, 4, 24, 168, 1284, 10384, 87364, 756808, 6704968, 60471040, 553334434, 5124366956, 47938322744, 452349133904, 4300336433872, 41148686798000, 396000558255084, 3830370110005728, 37218151946806512, 363109794135657408, 3555651588908143457, 34934228253014629644

Offset

1,3

Links

Table of n, a(n) for n=1..23.

Formula

Self-convolution yields A212392.

Example

 G.f.: A(x) = x + x^4 + 4*x^7 + 24*x^10 + 168*x^13 + 1284*x^16 + 10384*x^19 +...
such that
A(A(x)^2)^2 = x^4 + 4*x^7 + 24*x^10 + 168*x^13 + 1284*x^16 + 10384*x^19 +...
where
A(x)^2 = x^2 + 2*x^5 + 9*x^8 + 56*x^11 + 400*x^14 + 3096*x^17 + 25256*x^20 +...+ A212392(n)*x^(3*n-1) +...

Prog

 (PARI) {a(n)=local(A=x+x^4); for(i=1, n, A=x+subst(A^2, x, A^2+O(x^(3*n)))); polcoeff(A, 3*n-2)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A212392, A212391.

Sequence in context: A214377 A331007 A369503 * A246423 A188913 A364324

Adjacent sequences: A212274 A212275 A212276 * A212278 A212279 A212280

Keyword

nonn

Author

Paul D. Hanna, May 13 2012

Status

approved