A078819 a(n) = 140*C(2n,n)/(n+4).

35, 56, 140, 400, 1225, 3920, 12936, 43680, 150150, 523600, 1847560, 6584032, 23661365, 85652000, 312018000, 1142971200, 4207562730, 15557374800, 57750861000, 215145084000, 804104751450, 3014244096864, 11329763650800, 42691863032000, 161238018415500, 610258100044320

Offset

0,1

Links

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

Formula

D-finite with recurrence a(n) = a(n-1)*(4n^2+10n-6)/(n^2+4n) = A078817(n, 3) = 7*A078820(n)/(2n+1) = 140*A000984(n)/(n+4).

From Amiram Eldar, Feb 16 2023: (Start)

Sum_{n>=0} 1/a(n) = Pi/(126*sqrt(3)) + 3/70.

Sum_{n>=0} (-1)^n/a(n) = 37/1750 - 3*log(phi)/(125*sqrt(5)), where phi is the golden ratio (A001622). (End)

a(n) ~ 35 * 4^(n+1) / (n^(3/2) * sqrt(Pi)). - Amiram Eldar, Oct 10 2025

Example

a(5) = 140*C(10,5)/9 = 3920.

Mathematica

Table[140*Binomial[2*n, n]/(n + 4), {n, 0, 30}] (* Amiram Eldar, Feb 16 2023 *)

Crossrefs

Cf. A000108, A000984, A001622, A038629, A078817, A078818, A078820.

Sequence in context: A048033 A254366 A242291 * A189554 A351095 A267738

Adjacent sequences: A078816 A078817 A078818 * A078820 A078821 A078822

Keyword

nonn,easy

Author

Henry Bottomley, Dec 07 2002

Status

approved