A393524 Number of bicolored unordered increasing trees having n blue nodes and any number of red nodes, such that each red node has at least two children.

1, 2, 11, 116, 1993, 50674, 1788175, 83631728, 5007159389, 373508234222, 33966609134851, 3699141083849692, 475311338976310609, 71154473463028942634, 12276314165337164938775, 2418205713343385071245512, 539389515873083505589058725, 135250325619538564330152631462

Offset

1,2

Comments

Also the number of minimal inversion sequences for a pattern having a maximum diagonal difference of n-1 reached by its first entry (see the Testart reference).

Links

Benjamin Testart, Table of n, a(n) for n = 1..500

Benjamin Testart, On minimal pattern-containing inversion sequences, arXiv:2602.12130 [math.CO], 2026. See Section 5.1.

Example

Trees are written in parenthesized form v(c1,c2,...) with children listed in increasing order of labels. Each label carries a sign: '-' indicates the color blue and '+' indicates the color red. For n = 3, the 11 trees are: 1-(2-,3-), 1-(2-(3-)), 1-(2+(3-,4-)), 1+(2-,3-,4-), 1+(2-,3-(4-)), 1+(2-(4-),3-), 1+(2-(3-),4-), 1+(2-,3+(4-,5-)), 1+(2+(4-,5-),3-), 1+(2+(3-,5-)4-), 1+(2+(3-,4-),5-).

Crossrefs

Column sums of A393523.

Sequence in context: A269082 A378016 A380914 * A304639 A374140 A130222

Adjacent sequences: A393521 A393522 A393523 * A393525 A393526 A393527

Keyword

nonn

Author

Benjamin Testart, Feb 18 2026

Status

approved