OFFSET
1,1
COMMENTS
Numerator of a(n)/n! is A099904(n).
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = Sum_{i=1..n, j=1..n} (i^3 + j^3).
a(n) = 2*n*Sum_{k=1..n} k^3. - Gary Detlefs, Oct 26 2011
a(n) = (n^5 + 2*n^4 + n^3)/2. - Charles R Greathouse IV, Oct 27 2011
G.f.: 2*x*(1+12*x+15*x^2+2*x^3)/(1-x)^6. - Colin Barker, May 04 2012
From Amiram Eldar, Nov 02 2021: (Start)
Sum_{n>=1} 1/a(n) = 2*zeta(3) - Pi^2 + 8.
Sum_{n>=1} (-1)^(n+1)/a(n) = 3*zeta(3)/2 + 12*log(2) - Pi^2/6 - 8. (End)
EXAMPLE
a(3) = (1/2) * (2^3)*(2+1)^2 = 36.
(or)
a(3) = (1^3+1^3) + (1^3+2^3) + (2^3+1^3) + (2^3+2^3) = 36.
MAPLE
MATHEMATICA
Table[(n^5+2*n^4+n^3)/2, {n, 30}] (* Wesley Ivan Hurt, Feb 26 2014 *)
PROG
(PARI) a(n)=(n^5+2*n^4+n^3)/2 \\ Charles R Greathouse IV, Oct 27 2011
(Magma) [(n^5+2*n^4+n^3)/2: n in [1..30]]; // Wesley Ivan Hurt, May 25 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alexander Adamchuk, Oct 29 2004
STATUS
approved