OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
R. D. Carmichael and T. L. DeLand, Find the sum of the series 1^2 + 5^2 + 14^2 + 30^2 + ... + [n*(n+1)*(2*n+1)/6]^2, American Mathematical Monthly, Vol. 15, No. 6/7, Jun-Jul, 1908, pp. 132-133.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
O.g.f.: x*(1+18*x+42*x^2+18*x^3+x^4)/(1-x)^6.
E.g.f.: x*(3+33*x+51*x^2+20*x^3+2*x^4)*exp(x)/3.
a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6).
MATHEMATICA
Table[n^3 (2 n^2 + 1)/3, {n, 0, 40}]
PROG
(Magma) [n^3*(2*n^2+1)/3: n in [0..40]];
(PARI) vector(100, n, n--; n^3*(2*n^2+1)/3) \\ Altug Alkan, Apr 22 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Apr 22 2016
STATUS
approved