A101487 G.f. satisfies A(x) = x*(1+4A+A^2)^2/(1+A+A^2).

0, 1, 7, 59, 544, 5289, 53256, 549771, 5782105, 61698314, 666014200, 7257758425, 79716116408, 881431795012, 9802065031740, 109547572895811, 1229634981583560, 13855340183096319, 156654090794892216

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

M. Bousquet-Mélou, Limit laws for embedded trees

Formula

a(n) ~ Gamma(1/4) * 2^(2*n - 2) * 3^(n + 1/2) / (Pi * n^(5/4)) * (1 - 2*sqrt(3*Pi) / (Gamma(1/4) * n^(1/4)) + 15*Pi*sqrt(2) / (4*Gamma(1/4)^2 * sqrt(n))). - Vaclav Kotesovec, Nov 20 2017

Maple

A:= proc(n) option remember; if n=0 then 0 else convert(series(x* (1+ 4*A(n-1) +A(n-1)^2)^2/ (1+A(n-1) +A(n-1)^2), x, n+1), polynom) fi end: a:= n-> coeff(A(n), x, n): seq(a(n), n=0..18); # Alois P. Heinz, Aug 23 2008

Mathematica

A[n_] := A[n] = If[n==0, 0, Normal[Series[x*(1+4*A[n-1]+A[n-1]^2)^2/(1+A[n-1]+ A[n-1]^2), {x, 0, n+1}]]]; a[n_] := Coefficient[A[n], x, n]; Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Mar 30 2015, after Alois P. Heinz *)
CoefficientList[Series[(1 + Sqrt[1 - 12*x] - x*(8 + Sqrt[2]*Sqrt[(1 + Sqrt[1 - 12*x] - 2*(7 + 4*Sqrt[1 - 12*x])*x + 24*x^2) / x^2])) / (4*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Nov 20 2017 *)

Crossrefs

Sequence in context: A015568 A322667 A363105 * A210397 A099659 A358599

Adjacent sequences: A101484 A101485 A101486 * A101488 A101489 A101490

Keyword

nonn

Author

Ralf Stephan, Jan 21 2005

Status

approved