A116869 Sixth column of triangle A028364.

132, 297, 869, 2739, 8986, 30275, 104006, 362738, 1280592, 4566642, 16423581, 59497075, 216901454, 795117015, 2929034130, 10837075830, 40253156520, 150045410430, 561097823490, 2104382963214, 7913603390196, 29832744942302, 112719419791660, 426793102653764, 1619137259402432

Offset

0,1

Comments

Also sixth diagonal of triangle A067323.

Links

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

Formula

a(n) = A028364(n+5,5) = Sum_{k=0..5} C(k)*C(n+5-k), with the Catalan numbers C(n) = A000108(n).

G.f.: (c5(x)*c(x)-(c5(x)-1)/x)/x^5, with c5(x) = Sum_{k=0..5} C(k)*x^k and c(x) is the g.f. for the Catalan numbers A000108.

a(n) ~ 793 * 2^(2*n+1) / (n^(3/2) * sqrt(Pi)). - Amiram Eldar, Oct 09 2025

Mathematica

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

Crossrefs

Cf. A000108, A028364, A067296 (fifth column), A067323.

Sequence in context: A319274 A241754 A063365 * A035141 A205222 A116154

Adjacent sequences: A116866 A116867 A116868 * A116870 A116871 A116872

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 24 2006

Status

approved