A141351 a(n) = C(n) + 1 - 0^n where C(n) = A000108(n).

1, 2, 3, 6, 15, 43, 133, 430, 1431, 4863, 16797, 58787, 208013, 742901, 2674441, 9694846, 35357671, 129644791, 477638701, 1767263191, 6564120421, 24466267021, 91482563641, 343059613651, 1289904147325, 4861946401453, 18367353072153, 69533550916005

Offset: 0

Author

Paul Barry, Jun 27 2008

Keywords

• easy
• nonn

Comments

Hankel transform is A141352.

For n >= 2, a(n) is the number of parking functions of size n avoiding the patterns 132, 213, 231, and 312. - Lara Pudwell, Apr 12 2023

Links

• Ayomikun Adeniran and Lara Pudwell, Pattern avoidance in parking functions, Enumer. Comb. Appl. 3:3 (2023), Article S2R17.

Crossrefs

Cf. A000108, A057427, A141353.

Programs

Maple

a:= n-> signum(n)+binomial(n+n,n)/(n+1):
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 13 2023

Formula

G.f.: c(x) + x/(1-x), where c(x) is the g.f. of A000108.

Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(9*n-13)*a(n-2) +2*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Oct 15 2014

a(n) = A000108(n) + A057427(n). - Alois P. Heinz, Apr 13 2023