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

0,1

Comments

It appears that all terms are multiples of 99. - Michel Marcus, Aug 01 2015

Links

Table of n, a(n) for n=0..21.

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

Adjacent sequences: A104475 A104476 A104477 * A104479 A104480 A104481

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