A242009 G.f. satisfies: A(x) = 1 - x + A(x)^3 - A(x*A(x)^5).

1, 1, 2, 27, 540, 15273, 545424, 23441679, 1174939901, 67222626658, 4321856514871, 308474127741229, 24206976396414033, 2071823443548447053, 192096343794154776046, 19183353188372473420096, 2052995326868420586298713, 234422512754956257129580893

Offset

0,3

Comments

In general, if g.f. satisfies: A(x) = 1 - x + A(x)^3 - A(x*A(x)^q), q>=3, then a(n) ~ c(q) * q^n * n^(n - 3/q + (1/2-7/(2*q))*log(2)) / (exp(n) * (log(2))^n), where c(q) is a constant independent on n.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..330

Formula

a(n) ~ c * 5^n * n^(n - 3/5 - 1/5*log(2)) / (exp(n) * (log(2))^n), where c = 0.1494101265204548503053...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A = 2*A - (1-x + A^3 - subst(A, x, x*A^5 +x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A242007 (q=3), A242008 (q=4).

Sequence in context: A240638 A245050 A381775 * A121137 A203429 A153850

Adjacent sequences: A242006 A242007 A242008 * A242010 A242011 A242012

Keyword

nonn

Author

Vaclav Kotesovec, Aug 11 2014

Extensions

Name corrected by Vaclav Kotesovec and Paul D. Hanna, Aug 15 2014

Status

approved