A104478 a(n) = binomial(n+8,8)*binomial(n+12,8).

495, 11583, 135135, 1061775, 6370650, 31286970, 131405274, 486370170, 1621233900, 4946841900, 13992495660, 37058912748, 92647281870, 220089696750, 499568676750, 1088533853550, 2285921092455, 4642276728375, 9143878404375, 17513561154375, 32691980821500, 59592810754620

Offset: 0

Author

Zerinvary Lajos, Apr 18 2005

Keywords

• easy
• nonn

Comments

All terms are multiples of 99. - Michel Marcus, Aug 01 2015

Examples

			a(0): C(0+8,8)*C(0+12,8) = C(8,8)*C(12,8) = 1*495 = 495.
a(7): C(7+8,8)*C(7+12,8) = C(15,8)*C(19,8) = 6435*75582 = 486370170.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

Crossrefs

Cf. A000581, A062264.

Programs

Magma

[Binomial(n+8,8)*Binomial(n+12,8): n in [0..30]]; // Vincenzo Librandi, Jul 31 2015

Mathematica

f[n_] := Binomial[n + 8, 8] * Binomial[n + 12, 8]; Table[ f[n], {n, 0, 18}] (* Robert G. Wilson v, Apr 19 2005 *)

PARI

vector(30, n, n--; binomial(n+8,8)*binomial(n+12,8)) \\ Michel Marcus, Jul 31 2015

SageMath

def A104478(n): return binomial(n+8,8)*binomial(n+12,8)
print([A104478(n) for n in range(31)]) # G. C. Greubel, Mar 04 2025

Formula

a(n) = A000581(n+8)*A000581(n+12). - Michel Marcus, Aug 01 2015

From Amiram Eldar, Sep 04 2022: (Start)

Sum_{n>=0} 1/a(n) = 11648*Pi^2/3 - 65726161036/1715175.

Sum_{n>=0} (-1)^n/a(n) = 262144*log(2)/99 - 629604992/343035. (End)

G.f.: 99*(5 + 32*x + 56*x^2 + 32*x^3 + 5*x^4)/(1-x)^17. - G. C. Greubel, Mar 04 2025

Extensions

Corrected and extended by Robert G. Wilson v, Apr 19 2005

a(6) corrected by Georg Fischer, May 08 2021