Voozh

A050491

a(n) = C(n)*(12n+1) where C(n) = Catalan numbers (A000108).

1, 13, 50, 185, 686, 2562, 9636, 36465, 138710, 529958, 2032316, 7818538, 30161740, 116635300, 451980360, 1754766945, 6824030310, 26577181950, 103647597900, 404703270510, 1581953021220, 6189965556060, 24242879364600, 95027512981050, 372782298576636, 1463445866837052

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

REFERENCES

Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

FORMULA

G.f.: (11 - 20*x - 11*sqrt(1 - 4*x))/(2*x*sqrt(1 - 4*x)). - Amiram Eldar, Jul 08 2023

a(n) ~ 3 * 4^(n+1) / sqrt(Pi*n). - Amiram Eldar, Oct 11 2025

MATHEMATICA

Table[CatalanNumber[n] * (12*n + 1), {n, 0, 25}] (* Amiram Eldar, Jul 08 2023 *)