A241998 G.f. satisfies: A(x)^2 = x + A(x*A(x)^6).

1, 1, 5, 95, 2865, 115995, 5795546, 341588686, 23099712021, 1759081180848, 148827977847297, 13846375810530924, 1405013226803228823, 154447381376266478808, 18287299416725063983915, 2320814090889444342775833, 314320342934125785370051303

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Formula

a(n) ~ c * 6^n * n^(n - 1/6 + 1/4*log(2)) / (exp(n) * log(2)^n), where c = 0.1671159774327212...

Prog

(PARI) {a(n)=local(A=[1, 1], Ax); for(i=1, n, A=concat(A, 0); Ax=Ser(A);
A[#A]=Vec(1+subst(Ax, x, x*Ax^6) - Ax^2)[#A]); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A240996 (q=2), A240999 (q=3), A241996 (q=4), A241997 (q=5), A241999 (q=7).

Sequence in context: A363844 A233077 A182960 * A263394 A336942 A193478

Adjacent sequences: A241995 A241996 A241997 * A241999 A242000 A242001

Keyword

nonn

Author

Vaclav Kotesovec, Aug 11 2014

Status

approved