|
| |
|
|
A098848
|
|
a(n) = n*(n + 14).
|
|
19
|
|
|
|
0, 15, 32, 51, 72, 95, 120, 147, 176, 207, 240, 275, 312, 351, 392, 435, 480, 527, 576, 627, 680, 735, 792, 851, 912, 975, 1040, 1107, 1176, 1247, 1320, 1395, 1472, 1551, 1632, 1715, 1800, 1887, 1976, 2067, 2160, 2255, 2352, 2451, 2552, 2655, 2760, 2867
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = (n+7)^2 - 7^2 = n*(n + 14), n>=0.
G.f.: x*(15 - 13*x)/(1-x)^3.
Sum_{n>=1} 1/a(n) = 1171733/5045040 = 0.2322544518... via Sum_{n>=0} 1/((n+x)(n+y)) = (psi(x)-psi(y))/(x-y). - R. J. Mathar, Jul 14 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
E.g.f.: x*(15 + x)*exp(x). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 237371/5045040. - Amiram Eldar, Jan 15 2021
|
|
|
MATHEMATICA
|
LinearRecurrence[{3, -3, 1}, {0, 15, 32}, 50] (* G. C. Greubel, Jul 29 2016 *)
|
|
|
PROG
|
|
|
|
CROSSREFS
|
a(n-7), n>=8, seventh column (used for the n=7 series of the hydrogen atom) of triangle A120070.
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Eugene McDonnell (eemcd(AT)mac.com), Nov 04 2004
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
