OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
FORMULA
From R. J. Mathar, Jul 13 2009: (Start)
a(n) = 144 * A000579(n+5).
G.f.: 144*x/(1-x)^7. (End)
E.g.f.: x*(720 +1800*x +1200*x^2 +300*x^3 +30*x^4 +x^5)*exp(x)/5. - G. C. Greubel, Aug 27 2019
From Amiram Eldar, Jan 09 2022: (Start)
Sum_{n>=1} 1/a(n) = 1/120.
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/3 - 661/720. (End)
MAPLE
seq(144*binomial(n+5, 6), n = 0..30); # G. C. Greubel, Aug 27 2019
MATHEMATICA
CoefficientList[Series[144*x/(1-x)^7, {x, 0, 30}], x] (* Vincenzo Librandi, Mar 05 2012 *)
Table[(Times@@(n+Range[0, 5]))/5, {n, 0, 30}] (* Harvey P. Dale, Jul 01 2019 *)
144*Binomial[Range[30] +4, 6] (* G. C. Greubel, Aug 27 2019 *)
PROG
(Magma) [n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)/5: n in [1..30]]; // Vincenzo Librandi, Mar 05 2012
(PARI) vector(30, n, 144*binomial(n+4, 6)) \\ G. C. Greubel, Aug 27 2019
(Sage) [144*binomial(n+5, 6) for n in (0..30)] # G. C. Greubel, Aug 27 2019
(GAP) List([0..30], n-> 144*Binomial(n+5, 6)); # G. C. Greubel, Aug 27 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jul 10 2009
EXTENSIONS
Definition factorized, offset corrected by R. J. Mathar, Jul 13 2009
STATUS
approved