A390398 a(2) = 4; for n >= 3, a(n) = a(n-1)*(a(n-1) - 1)/2 + 2.

4, 8, 30, 437, 95268, 4537948280, 10296487293708505062, 53008825294750347287511923230585559393, 1404967779564682121491827836997988245548146456503546321053236877676072484530

Offset

2,1

Comments

For n>=2, a(n) is the Colijn-Plazzotta rank of the pseudocaterpillar unlabeled binary rooted tree with tree height n and n+2 leaves.

Links

Table of n, a(n) for n=2..10.

Luc Devroye, Michael R. Doboli, Noah A. Rosenberg, Stephan Wagner, Tree height and the asymptotic mean of the Colijn-Plazzotta rank of unlabeled binary rooted trees, Bull. Math. Biol. 87 (2025), 172. See p. 11.

Mathematica

RecurrenceTable[{a[2] == 4, a[n] == a[n - 1] (a[n - 1] - 1)/2 + 2}, a[n], {n, 10}]

Crossrefs

Cf. A108225.

Sequence in context: A317583 A020331 A248476 * A082595 A262154 A080072

Adjacent sequences: A390395 A390396 A390397 * A390399 A390400 A390401

Keyword

nonn

Author

Noah A Rosenberg, Nov 04 2025

Status

approved