|
| |
|
|
A141013
|
|
E.g.f. Sum_{d|M} (exp(d*x)-1)/d, M=14.
|
|
3
|
|
|
|
0, 4, 24, 250, 3096, 40834, 554664, 7647250, 106237176, 1481554114, 20701400904, 289537131250, 4051542498456, 56707753666594, 793811662272744, 11112685048647250, 155572843119354936
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = sum_{d|14} d^(n-1) = 1+2^(n-1)+7^(n-1)+14^(n-1).
a(n)= 24*a(n-1) -163*a(n-2) +336*a(n-3) -196*a(n-4), n>4.
G.f: -2*x*(-2+36*x-163*x^2+168*x^3)/((x-1)*(14*x-1)*(2*x-1)*(7*x-1)).
(End)
|
|
|
MAPLE
|
A141013 := proc(n) local d; add(d^(n-1), d=numtheory[divisors](14)) ; end proc: seq(A141013(n), n=1..20) ; # R. J. Mathar, Mar 05 2010
|
|
|
MATHEMATICA
|
CoefficientList[Series[- 2 x (-2 + 36 x - 163 x^2 + 168 x^3)/((x-1) (14*x-1) (2*x-1) (7*x-1)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 12 2012 *)
|
|
|
PROG
|
(Magma) [0] cat [1+2^(n-1)+7^(n-1)+14^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 12 2012
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
