OFFSET
0,4
LINKS
Julien Rouyer, Table of n, a(n) for n = 0..47
FORMULA
With P the generating function of A363448, the generating function Q of (a(n)) is a solution of the system of two equations
P(t)=Q(t)/(1-Q(t))+t/(1-Q(t))^2+1
Q(t)=t/(1-tP(t))-t.
EXAMPLE
For n=3, the a(3)=2 partitions are {{1,3},{2}} and {{1,2,3}}.
For n=4, the a(4)=4 partitions are {{1,4},{2,3}}, {{1,2,4},{3}}, {{1,3,4},{2}} and {{1,2,3,4}}.
PROG
(Sage) t, P, Q = var('t, P, Q')
P = Q / ( 1 - Q ) + t / ( 1 - Q )^2 + 1
solQ=solve([Q == t / (1 - t * P) - t], Q)
q=solQ[1].rhs()
n = 47
DL_Q = (taylor(q, t, 0, n)).simplify_full()
Qn = DL_Q.list()
# Julien Rouyer, Wenjie Fang, and Alain Ninet, Jun 17 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Julien Rouyer, Jun 17 2024
STATUS
approved