OFFSET
0,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
G.f.: (1+5*x)/(1-x)^8.
a(0)=1, a(1)=13, a(2)=76, a(3)=300, a(4)=930, a(5)=2442, a(6)=5676, a(7)=12012, a(n) = 8*a(n-1) -28*a(n-2) +56*a(n-3) -70*a(n-4) +56*a(n-5) -28*a(n-6) +8*a(n-7) -a(n-8). - Harvey P. Dale, Jul 29 2014
MAPLE
seq((6*n+7)*binomial(n+6, 6)/7, n=0..30); # G. C. Greubel, Aug 28 2019
MATHEMATICA
Accumulate[Table[(n+1)Binomial[n+5, 5], {n, 0, 30}]] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 13, 76, 300, 930, 2442, 5676, 12012}, 30] (* Harvey P. Dale, Jul 29 2014 *)
CoefficientList[Series[(1+5x)/(1-x)^8, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 30 2014 *)
PROG
(Magma) [(6*n+7)*Binomial(n+6, 6)/7: n in [0..40]]; // Vincenzo Librandi, Jul 30 2014
(PARI) a(n)=(6*n/7+1)*binomial(n+6, 6) \\ Charles R Greathouse IV, Oct 07 2015
(Sage) [(6*n+7)*binomial(n+6, 6)/7 for n in (0..30)] # G. C. Greubel, Aug 28 2019
(GAP) List([0..30], n-> (6*n+7)*Binomial(n+6, 6)/7); # G. C. Greubel, Aug 28 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Corrected and extended by N. J. A. Sloane, Apr 21 2000
STATUS
approved