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

0,3

Comments

Previous name was: A simple grammar.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 729

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)

Maple

spec := [S, {S=Prod(Z, B, B, B, B), B=PowerSet(S)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);

Crossrefs

Column k=4 of A255517.

Sequence in context: A083410 A295553 A302548 * A365124 A371496 A052650

Adjacent sequences: A052769 A052770 A052771 * A052773 A052774 A052775

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

New name from Vaclav Kotesovec, Feb 24 2015

Status

approved