OFFSET
0,1
COMMENTS
All terms are multiples of 99. - Michel Marcus, Aug 01 2015
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).
FORMULA
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
EXAMPLE
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.
MATHEMATICA
f[n_] := Binomial[n + 8, 8] * Binomial[n + 12, 8]; Table[ f[n], {n, 0, 18}] (* Robert G. Wilson v, Apr 19 2005 *)
PROG
(PARI) vector(30, n, n--; binomial(n+8, 8)*binomial(n+12, 8)) \\ Michel Marcus, Jul 31 2015
(Magma) [Binomial(n+8, 8)*Binomial(n+12, 8): n in [0..30]]; // Vincenzo Librandi, 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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Apr 18 2005
EXTENSIONS
Corrected and extended by Robert G. Wilson v, Apr 19 2005
a(6) corrected by Georg Fischer, May 08 2021
STATUS
approved