A242004 G.f. satisfies: 2*A(x) = 1 + x + A(x*A(x)^2).

1, 1, 2, 13, 136, 1901, 32672, 660213, 15261866, 396260409, 11404802292, 360239943502, 12389377190088, 460921028363253, 18446977179761746, 790450173217191235, 36112553368752540450, 1752531204026383726825, 90044479726218309099544, 4883556796657253767140501

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..320

Formula

a(n) ~ c * 2^n * n^(n + 1/4*log(2)) / (exp(n) * (log(2))^n), where c = 0.52809869533428510...

Mathematica

nmax = 19; sol = {a[0] -> 1};
Do[A[x_] = Sum[a[k] x^k, {k, 0, n}] /. sol; eq = CoefficientList[2 A[x] - (1 + x + A[x A[x]^2]) + O[x]^(n + 1), x] == 0 /. sol; sol = sol ~Join~ Solve[eq][[1]], {n, 1, nmax}];
sol /. Rule -> Set;
a /@ Range[0, nmax] (* Jean-François Alcover, Nov 01 2019 *)

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A = 1+x + subst(A, x, x*A^2 +x*O(x^n)) - A); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A242003 (q=1), A242005 (q=3), A242006 (q=4).

Sequence in context: A065132 A047856 A246875 * A187021 A152059 A132063

Adjacent sequences: A242001 A242002 A242003 * A242005 A242006 A242007

Keyword

nonn

Author

Vaclav Kotesovec, Aug 11 2014

Extensions

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

Status

approved