OFFSET
0,2
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: x*(4 +15*x +5*x^2)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009
E.g.f.: x*(24 + 81*x + 47*x^2 + 6*x^3)*exp(x)/6. - G. C. Greubel, Mar 03 2020
From Amiram Eldar, Mar 10 2022: (Start)
Sum_{n>=1} 1/a(n) = 36 - 9*sqrt(3)*Pi/2 + 48*log(2) - 81*log(3)/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = (9*sqrt(3)-12)*Pi - 36*(1-log(2)). (End)
MAPLE
seq( n*mul(j*n+1, j=1..3)/6, n=0..40); # G. C. Greubel, Mar 03 2020
MATHEMATICA
Table[n(n+1)(2n+1)(3n+1)/6, {n, 0, 40}] (* Harvey P. Dale, Feb 24 2011 *)
PROG
(PARI) vector(41, n, my(m=n-1); m*prod(j=1, 3, j*m+1)/6) \\ G. C. Greubel, Mar 03 2020
(Magma) [n*(&*[j*n+1:j in [1..3]])/6: n in [0..40]]; // G. C. Greubel, Mar 03 2020
(Sage) [n*product(j*n+1 for j in (1..3))/6 for n in (0..40)] # G. C. Greubel, Mar 03 2020
(GAP) List([0..40], n-> n*(n+1)*(2*n+1)*(3*n+1)/6 ); # G. C. Greubel, Mar 03 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved