A241997 G.f. satisfies: A(x)^2 = x + A(x*A(x)^5).

1, 1, 4, 62, 1530, 50849, 2089719, 101470053, 5660430287, 355970992756, 24894562936569, 1915987357589537, 160941576221849622, 14653841416756810665, 1437868649635368258342, 151284341822917527109841, 16993002921809143802858179, 2029842747191877113876104045

Offset

0,3

Links

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

Formula

a(n) ~ c * 5^n * n^(n - 1/5 + 1/5*log(2)) / (exp(n) * log(2)^n), where c = 0.2007164067804229...

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^5) - Ax^2)[#A]); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A240996 (q=2), A240999 (q=3), A241996 (q=4), A241998 (q=6), A241999 (q=7).

Sequence in context: A222791 A166028 A359620 * A332694 A277392 A349068

Adjacent sequences: A241994 A241995 A241996 * A241998 A241999 A242000

Keyword

nonn

Author

Vaclav Kotesovec, Aug 11 2014

Status

approved