A104476 a(n) = binomial(n+7,7)*binomial(n+11,7).

330, 6336, 61776, 411840, 2123550, 9060480, 33372768, 109219968, 324246780, 886828800, 2261413440, 5427392256, 12352970916, 26829982080, 55895796000, 112183843200, 217706770710, 409800980160, 750266946000, 1339149240000, 2335141487250, 3985308138240

Offset: 0

Author

Zerinvary Lajos, Apr 18 2005

Keywords

• easy
• nonn

Examples

			a(0): C(0+7,7)*C(0+11,7) = C(7,7)*C(11,7) = 1*330 = 330;
a(7): C(7+7,7)*C(7+11,7) = C(14,7)*C(18,7) = 3432*31824 = 109219968.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Crossrefs

Cf. A062264.

Programs

Magma

[Binomial(n+7,7)*Binomial(n+11,7): n in [0..30]]; // Vincenzo Librandi, Jul 31 2015

Mathematica

f[n_] := Binomial[n + 7, 7]*Binomial[n + 11, 7]; Table[ f[n], {n, 0, 19}] (* Robert G. Wilson v, Apr 20 2005 *)

PARI

vector(30, n, n--; binomial(n+7,7)*binomial(n+11,7)) \\ Michel Marcus, Jul 31 2015

Python

A104476_list, m = [], [3432, -1716, 660, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330]
for _ in range(10**2):
    A104476_list.append(m[-1])
    for i in range(14):
        m[i+1] += m[i] # Chai Wah Wu, Dec 15 2015

SageMath

def A104476(n): return binomial(n+7,7)*binomial(n+11,7)
print([A104476(n) for n in range(31)]) # G. C. Greubel, Mar 04 2025

Formula

From Amiram Eldar, Sep 01 2022: (Start)

Sum_{n>=0} 1/a(n) = 539*Pi^2 - 114905813/21600.

Sum_{n>=0} (-1)^n/a(n) = 1741019/7200 - 49*Pi^2/2. (End)

G.f.: 66*(5 + 21*x + 21*x^2 + 5*x^3)/(1-x)^15. - G. C. Greubel, Mar 04 2025

Extensions

More terms from Robert G. Wilson v, Apr 20 2005