OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (49,-1029,12005,-84035,352947,-823543,823543).
FORMULA
a(n) = 7^(n-1)*binomial(n+7, 6).
G.f.: (-1 + (1-7*x)^(-7))/(x*7^2).
From Amiram Eldar, Nov 03 2025: (Start)
Sum_{n>=0} 1/a(n) = 12334378/5 - 16003008*log(7/6).
Sum_{n>=0} (-1)^n/a(n) = 45024483/5 - 67436544*log(8/7). (End)
MATHEMATICA
CoefficientList[Series[(-1+1/(1-7x)^7)/(49x), {x, 0, 30}], x] (* or *) LinearRecurrence[{49, -1029, 12005, -84035, 352947, -823543, 823543}, {1, 28, 588, 10290, 158466, 2218524, 28840812}, 30] (* Harvey P. Dale, Jun 03 2015 *)
Table[7^(n-1)*Binomial[n+7, 6], {n, 0, 30}] (* G. C. Greubel, Aug 16 2018 *)
PROG
(SageMath)[lucas_number2(n, 7, 0)*binomial(n, 6)/7^8 for n in range(7, 24)] # Zerinvary Lajos, Mar 13 2009
(PARI) vector(30, n, n--; 7^(n-1)*binomial(n+7, 6)) \\ G. C. Greubel, Aug 16 2018
(Magma) [7^(n-1)*Binomial(n+7, 6): n in [0..30]]; // G. C. Greubel, Aug 16 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved