A242003 G.f. satisfies: 2*A(x) = 1 + x + A(x*A(x)).

1, 1, 1, 3, 15, 101, 841, 8267, 93259, 1184693, 16718377, 259403303, 4389247891, 80446526037, 1587992497445, 33595010710967, 758426286470763, 18201458396436081, 462778682120158733, 12427549693656564655, 351513706699979429223, 10446113259707687607057

Offset

0,4

Links

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

Formula

a(n) ~ c * n^n / (exp(n) * (log(2))^n), where c = 1.16670181891916121...

Mathematica

nmax = 21; 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]]) + 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 +x*O(x^n)) - A); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A242004 (q=2), A242005 (q=3), A242006 (q=4).

Cf. A006196.

Sequence in context: A074536 A152093 A109777 * A265164 A348793 A135903

Adjacent sequences: A242000 A242001 A242002 * A242004 A242005 A242006

Keyword

nonn

Author

Vaclav Kotesovec, Aug 11 2014

Extensions

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

Status

approved