A172510 a(n) = binomial(n + 4, 4) * 8^n.
1, 40, 960, 17920, 286720, 4128768, 55050240, 692060160, 8304721920, 95965675520, 1074815565824, 11725260718080, 125069447659520, 1308418837053440, 13458022323978240, 136374626216312832, 1363746262163128320, 13477021884906209280, 131775325096860712960
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..138
- Index entries for linear recurrences with constant coefficients, signature (40,-640,5120,-20480,32768).
Programs
-
Magma
[Binomial(n + 4, 4)*8^n: n in [0..30]]; // Vincenzo Librandi, Jun 06 2011
-
Mathematica
Table[Binomial[n + 4, 4]*8^n, {n, 0, 25}] -
PARI
Vec(1 / (1-8*x)^5 + O(x^30)) \\ Colin Barker, Jul 24 2017
Formula
G.f.: 1 / (1-8*x)^5. - R. J. Mathar, Feb 11 2010
a(n) = (8^(-1 + n)*(1 + n)*(2 + n)*(3 + n)*(4 + n)) / 3. - Colin Barker, Jul 24 2017
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 4400/3 - 10976*log(8/7).
Sum_{n>=0} (-1)^n/a(n) = 23328*log(9/8) - 8240/3. (End)