A241996 G.f. satisfies: A(x)^2 = x + A(x*A(x)^4).

1, 1, 3, 36, 691, 17953, 578590, 22086434, 970562211, 48162981790, 2661660956118, 162076663712956, 10782672104108188, 778258213420732537, 60580553895367923682, 5059770644086584978690, 451410973011659727975191, 42848908650336118172791330

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..260

Formula

a(n) ~ c * 4^n * n^(n - 1/4 + 1/8*log(2)) / (exp(n) * log(2)^n), where c = 0.2494094681962255...

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^4) - Ax^2)[#A]); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A240996 (q=2), A240999 (q=3), A241997 (q=5), A241998 (q=6), A241999 (q=7).

Sequence in context: A224256 A223912 A224184 * A366004 A006587 A328122

Adjacent sequences: A241993 A241994 A241995 * A241997 A241998 A241999

Keyword

nonn

Author

Vaclav Kotesovec, Aug 11 2014

Status

approved