A361039 a(n) = 55440 * (3*n)!/((2*n)!*(n+4)!).

2310, 1386, 2310, 5544, 16335, 55055, 204204, 813960, 3432198, 15142050, 69334650, 327523680, 1588667850, 7883530578, 39904290580, 205532444040, 1075067283906, 5701114384350, 30608320603770, 166169731127400, 911270544740325

Offset

0,1

Comments

Compare with the super ballot numbers A348893(n) = 840*(2*n)!/(n!*(n+4)!).

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = 2310*binomial(3*n,n) - 2057*binomial(3*n,n+1) + 627*binomial(3*n,n+2) - 102*binomial(3*n,n+3) + 7*binomial(3*n, n+4). Thus a(n) is an integer.

P-recursive: 2*(n + 4)*(2*n - 1) = 3*(3*n - 1)*(3*n - 2)*a(n-1) with a(0) = 2310.

a(n) ~ (27/4)^n * 27720*sqrt(3/Pi)/n^(9/2).

The o.g.f. satisfies the differential equation

x^2*(27*x - 4)*A''(x) + 2*x*(27*x - 9)*A'(x) + (6*x + 8)*A(x) - 18480 = 0, with A(0) = 2310 and A'(0) = 1386.

Maple

seq(  55440 * (3*n)!/((2*n)!*(n+4)!), n = 0..20);

Crossrefs

Cf. A000139, A001764, A007226, A007272, A361037, A361038, A361041.

Sequence in context: A060231 A285487 A285744 * A051270 A046387 A136154

Adjacent sequences: A361036 A361037 A361038 * A361040 A361041 A361042

Keyword

nonn,easy

Author

Peter Bala, Mar 04 2023

Status

approved