A121516 Number of 3-decomposable trees on 3n nodes.

2, 10, 84, 788, 8188, 90110, 1035456, 12269932, 148886048, 1840585914, 23099713808, 293535000452, 3769200628592, 48831588116862, 637501117219024, 8378367468484212, 110760388293651950, 1471854299855109782, 19649723961974718686, 263422552838889748560

Offset

1,1

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..100

S. G. Wagner, An identity for the cycle indices of rooted tree automorphism groups, Elec. J. Combinat., 13 (2006), #R00.

Formula

Wagner gives a g.f.

a(n) ~ c * d^n / n^(3/2), where d = 14.47726020066578... and c = 0.144218531921... - Vaclav Kotesovec, Apr 07 2020

Maple

Nmax := 30 : nmax := 3*Nmax+1 : a := array(0..nmax) ; Dx := proc(z) global nmax, a ; local resul, i ; resul := 0 ; for i from 1 to (nmax+1)/3 do resul := resul+a[3*i]*z^(3*i) : od : RETURN(resul) ; end: exp1 := proc() global nmax, a ; local m, t ; t := 0 ; for m from 1 to nmax do t := t+3*Dx(x^m)/m ; od: return( taylor(exp(t), x=0, nmax+1) ) ; end: exp2 := proc() global nmax, a ; local m, t ; t := 0 ; for m from 1 to nmax do t := t+(Dx(x^m)+Dx(x^(2*m)))/m ; od: return( taylor(exp(t), x=0, nmax+1) ) ; end: DD := Dx(x)-3*x^3*exp1()/2-x^3*exp2()/2 : for i from 0 to nmax do a[i] := solve(coeftayl(DD, x=0, i), a[i]) ; if i mod 3 = 0 then print(a[i]) ; fi ; end: # R. J. Mathar, Sep 17 2006

Mathematica

terms = 20; A[_] = 0;
Do[A[x_] = (3x^3/2)Exp[Sum[(3/m)A[x^m], {m, 3 terms}]]+(x^3/2)Exp[Sum[(1/m) (A[x^m]+A[x^(2m)]), {m, 3terms}]] + O[x]^(3terms+1) // Normal, 3terms+1];
DeleteCases[CoefficientList[A[x], x], 0] (* Jean-François Alcover, Apr 07 2020 *)

Crossrefs

Cf. A000151.

Sequence in context: A101878 A121194 A302572 * A024491 A250117 A244627

Adjacent sequences: A121513 A121514 A121515 * A121517 A121518 A121519

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 12 2006

Extensions

More terms from R. J. Mathar, Sep 17 2006

Status

approved