A088791 Coefficient of x^n in A(x)^n is A000670(n), which gives preferential arrangements of n labeled elements.

1, 1, 1, 2, 8, 46, 337, 2976, 30627, 359222, 4725968, 68903766, 1102712316, 19219507328, 362428546833, 7352854216056, 159705991698432, 3697928742242694, 90933523698184947, 2366758931071064064

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..333

Formula

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

a(n) ~ (n-1)! / (4 * (log(2))^(n+1)). - Vaclav Kotesovec, Feb 12 2015

O.g.f.: A(x) = x/( series reversion x*B(x) ), where B(x) = 1 + x + 2*x^2 + 6*x^3 + 25*x^4 + 137*x^5 + ... is the o.g.f. of A084784. - Peter Bala, Jun 23 2015

Mathematica

nmax = 19; sol = {a[0] -> 1};
Do[A[x_] = Sum[a[k] x^k, {k, 0, n}] /. sol; eq = CoefficientList[A[x]^2 - (A[x A[x]] + 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 02 2019 *)

Prog

(PARI) {a(n)=local(A, m); if(n<1, n==0, m=1; A=1+x; for(i=1, n, A=(subst(A, x, x*A+x*O(x^n)) + x*A)/A); polcoeff(A, n))}
for(n=0, 20, print1(a(n), ", ")) \\ Vaclav Kotesovec, Feb 11 2015

Crossrefs

Cf. A000670, A084784.

Sequence in context: A005840 A161881 A219358 * A111552 A321965 A229559

Adjacent sequences: A088788 A088789 A088790 * A088792 A088793 A088794

Keyword

nonn,easy

Author

Paul D. Hanna, Oct 16 2003

Status

approved