A085375 a(n) = binomial(2*n+1, n+1)*binomial(n+4, 4).

1, 15, 150, 1225, 8820, 58212, 360360, 2123550, 12033450, 66050270, 353068716, 1845586470, 9464546000, 47738754000, 237329805600, 1164893795820, 5653161067950, 27157342385250, 129275302348500, 610315506350550, 2859764086899720, 13308425945529000

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Jun 26 2003

Keywords

• easy
• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A001700, A002457, A085373, A085374.

Cf. A000332, A000984.

Programs

Maple

seq(binomial(2*n+1, n+1)*binomial(n+4, 4), n=0..20); # Zerinvary Lajos, Jan 18 2007

Mathematica

Table[Binomial[2*n + 1, n + 1] * Binomial[n + 4, 4], {n, 0, 30}]

Python

from _future_ import division
A085375_list, b = [], 1
for n in range(501):
    A085375_list.append(b)
    b = b*2*(n+5)*(2*n+3)//((n+1)*(n+2)) # Chai Wah Wu, Jan 26 2016

Formula

a(n+1) = a(n)*2*(n+5)*(2*n+3)/((n+1)*(n+2)). - Chai Wah Wu, Jan 26 2016

G.f.: (1 - 3*x + 6*x^2 - 5*x^3) / (1 - 4*x)^(9/2). - Ilya Gutkovskiy, Nov 17 2021