A156125 a(n) = 10^n*C(2n,n)/C(n+3,3).

1, 5, 60, 1000, 20000, 450000, 11000000, 286000000, 7800000000, 221000000000, 6460000000000, 193800000000000, 5943200000000000, 185725000000000000, 5899500000000000000, 190095000000000000000, 6203100000000000000000, 204702300000000000000000, 6823410000000000000000000

Offset

0,2

Comments

Hankel transform is 10^(n^2-1+0^n)*A156126(n).

Links

Table of n, a(n) for n=0..18.

Formula

G.f.: F(1/2,1;4;40x);

a(n) = 6*10^n*A000108(n)/((n+2)(n+3)) = 10^(n-1)*A007272(n).

(n+3)*a(n) + 20*(1-2*n)*a(n-1) = 0. - R. J. Mathar, Oct 25 2012

From Amiram Eldar, Sep 24 2025: (Start)

a(n) = 10^n * A000984(n) * A000292(n+1).

a(n) ~ 3 * 2^(3*n+1) * 5^n / (n^(7/2) * sqrt(Pi)).

Sum_{n>=0} 1/a(n) = 891580/771147 + 5600000*arccosec(2*sqrt(10))/(2313441*sqrt(39)).

Sum_{n>=0} (-1)^n/a(n) = 7328180/8477283 - 5600000*arccosech(2*sqrt(10))/(2825761*sqrt(41)). (End)

Mathematica

Table[10^n Binomial[2n, n]/Binomial[n+3, 3], {n, 0, 20}] (* Harvey P. Dale, Mar 30 2022 *)

Crossrefs

Cf. A000108, A000292, A000984, A007272, A011557, A156126.

Sequence in context: A234528 A380213 A277300 * A260776 A128574 A120976

Adjacent sequences: A156122 A156123 A156124 * A156126 A156127 A156128

Keyword

easy,nonn

Author

Paul Barry, Feb 04 2009

Status

approved