login
A104478
a(n) = binomial(n+8,8)*binomial(n+12,8).
0
495, 11583, 135135, 1061775, 6370650, 31286970, 131405274, 486370170, 1621233900, 4946841900, 13992495660, 37058912748, 92647281870, 220089696750, 499568676750, 1088533853550, 2285921092455, 4642276728375, 9143878404375, 17513561154375, 32691980821500, 59592810754620
OFFSET
0,1
COMMENTS
It appears that all terms are multiples of 99. - Michel Marcus, Aug 01 2015
LINKS
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
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)
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
CROSSREFS
Cf. A000581.
Sequence in context: A055160 A055157 A027808 * A133352 A140913 A214555
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