A339648 Number of series reduced trees with n nodes and integer labeled leaves covering an initial interval of positive integers.

1, 0, 2, 4, 16, 62, 290, 1496, 8548, 53278, 359076, 2597052, 20034252, 163996372, 1418326160, 12911494594, 123317867572, 1232219079760, 12848961783474, 139505358593240, 1573914932077692, 18418287165450500, 223191801317514104, 2796501582165674166, 36179439053130339742

Offset

1,3

Comments

Only leaves are labeled.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Example

a(4) = 4: (111), (112), (122), (123).
a(5) = 16: (1111), (1112), (1122), (1123), (1222), (1223), (1233), (1234), (1(11)), (1(12)), (1(22)), (1(23)), (2(11)), (2(12)), (2(13)), (3(12)).

Prog

(PARI) \\ here R(n, k) gives number of colorings with k colors as vector.
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
R(n, k)={my(v=vector(n)); v[1]=k; for(n=2, #v, v[n] = EulerT(concat(v[1..n-2], [0]))[n-1]); v}
seq(n)={sum(k=1, n, R(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)))}

Crossrefs

Cf. A001678 (uncolored), A318231 (inequivalent colorings).

Sequence in context: A152876 A153963 A153960 * A005027 A153969 A153966

Adjacent sequences: A339645 A339646 A339647 * A339649 A339650 A339651

Keyword

nonn

Author

Andrew Howroyd, Dec 11 2020

Status

approved