A052772 Number of rooted identity trees with n nodes and 4-colored non-root nodes.
0, 1, 4, 22, 156, 1193, 9748, 82916, 727088, 6524084, 59620732, 552970626, 5191935808, 49252903050, 471358286352, 4545310993994, 44121116086052, 430777978197156, 4227634212037728, 41680927531643928, 412638233333973820, 4100336181515969163, 40882494461218775272
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 729
Crossrefs
Column k=4 of A255517.
Programs
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Maple
spec := [S,{S=Prod(Z,B,B,B,B),B=PowerSet(S)},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);
Formula
a(n) ~ c * d^n / n^(3/2), where d = 10.68849275496965245845204879846824293047921245695819153804780100052532088..., c = 0.097992887955331161579155538221616838965194192139... . - Vaclav Kotesovec, Feb 24 2015
From Ilya Gutkovskiy, Apr 13 2019: (Start)
G.f. A(x) satisfies: A(x) = x*exp(4*Sum_{k>=1} (-1)^(k+1)*A(x^k)/k).
G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * Product_{n>=1} (1 + x^n)^(4*a(n)). (End)
Extensions
New name from Vaclav Kotesovec, Feb 24 2015
Comments