A067326 Fifth column of triangle A067323.

14, 56, 202, 715, 2529, 8986, 32123, 115556, 418200, 1521976, 5567551, 20462525, 75528895, 279874350, 1040790135, 3883140600, 14531382060, 54529456320, 205146226200, 773608833894, 2923686178098, 11071970477876, 42009145079502, 159673634222680, 607916275833440

Offset

0,1

Comments

Also fifth diagonal of triangle A028364.

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = A067323(n+4, 4) = C(n+5) - Sum_{k=0..3} C(k)*C(n+4-k), C(n) = A000108(n) (Catalan numbers).

G.f.: (c(x)^3)*(5+5*c(x)+3*c(x)^2+c(x)^3), with c(x) the g.f. of A000108 (Catalan numbers).

a(n) ~ 163 * 4^(n+1) / (n^(3/2) * sqrt(Pi)). - Amiram Eldar, Oct 09 2025

Mathematica

With[{c = CatalanNumber}, a[n_] := c[n+5] - Sum[c[k] * c[n+4-k], {k, 0, 3}]; Array[a, 25, 0]] (* Amiram Eldar, Oct 09 2025 *)

Crossrefs

Cf. A000108, A028364, A067323, A067325 (fourth column).

Sequence in context: A115129 A281200 A212341 * A202242 A041374 A070741

Adjacent sequences: A067323 A067324 A067325 * A067327 A067328 A067329

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 05 2002

Status

approved