A113894 a(n) = binomial(2*n, n) * binomial(2*n+5, n).

1, 14, 216, 3300, 50050, 756756, 11435424, 172931616, 2618916300, 39731777800, 603923022560, 9197348345640, 140334704005860, 2145155731845000, 32847841152720000, 503812888080163200, 7739375660195721300, 119063197872768778200, 1834199559285273180000

Offset: 0

Author

Zerinvary Lajos, Jan 28 2006

Keywords

• easy
• nonn

Examples

			a(0) = C(0,0)*C(5,0) = 1*1 = 1.
a(4) = C(8,4)*C(13,4) = 70*715 = 50050.
a(10) = C(20,10)*C(25,10) = 184756*3268760 = 603923022560.
		

Links

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

Crossrefs

Cf. A062190.

Programs

Magma

A113894:= func< n | (n+1)*Catalan(n)*Binomial(2*n+5,n) >;
[A113894(n): n in [0..30]]; // G. C. Greubel, Mar 01 2025

Mathematica

Table[Binomial[2n,n]Binomial[2n+5,n],{n,0,20}] (* Harvey P. Dale, Apr 11 2020 *)

PARI

a(n) = {binomial(2*n, n) * binomial(5+2*n, n)} \\ Andrew Howroyd, Jan 07 2020

SageMath

def A113894(n): return binomial(2*n,n)*binomial(2*n+5,n)
print([A113894(n) for n in range(31)]) # G. C. Greubel, Mar 01 2025

Formula

a(n) = A062190(2*n, n).

Extensions

Name edited and terms a(13) and beyond from Andrew Howroyd, Jan 07 2020