A067325 Fourth column of triangle A067323.

5, 19, 66, 227, 785, 2739, 9646, 34268, 122706, 442510, 1605956, 5861481, 21502585, 79243395, 293246550, 1089264360, 4059928950, 15179606010, 56917649820, 213982542150, 806429435994, 3046017513198, 11529383296076, 43724443147752, 166123154959300, 632226007840700

Offset

0,1

Comments

Also fourth diagonal of triangle A028364.

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = A067323(n+3, 3) = C(n+4) - (C(n+3)+C(n+2)+2*C(n+1)), C(n) = A000108(n) (Catalan numbers).

G.f.: (c(x)^3)*(2+2*c(x)+c(x)^2), with c(x) the g.f. of A000108 (Catalan numbers).

a(n) ~ 21 * 2^(2*n+3) / (n^(3/2) * sqrt(Pi)). - Amiram Eldar, Oct 09 2025

Mathematica

With[{c = CatalanNumber}, a[n_] := c[n+4] - Sum[c[k] * c[n+3-k], {k, 0, 2}]; Array[a, 25, 0]] (* Amiram Eldar, Oct 09 2025 *)

Crossrefs

Cf. A000108, A067323, A067324 (third column).

Sequence in context: A137745 A382989 A005021 * A273599 A347311 A121525

Adjacent sequences: A067322 A067323 A067324 * A067326 A067327 A067328

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 05 2002

Status

approved