OFFSET
1,1
REFERENCES
Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 162.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
Pedro A. Piza, Powers of sums and sums of powers, Math. Mag. 25 (3) (1952) 137.
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
a(n) = 3*(Sum_{k=1..n} k*(k+1)/2)^3.
a(n) = 3*A000292(n)^3.
G.f.: 3*x*(1+54*x+405*x^2+760*x^3+405*x^4+54*x^5+x^6) / (x-1)^10. - R. J. Mathar, Dec 13 2011
From Amiram Eldar, Apr 09 2024: (Start)
Sum_{n>=1} 1/a(n) = 261/4 - 54*zeta(3).
Sum_{n>=1} (-1)^(n+1)/a(n) = 135*zeta(3)/2 + 432*log(2) - 1521/4. (End)
MATHEMATICA
Array[#^3*(#+1)^3*(#+2)^3/72 &, 50] (* Paolo Xausa, Apr 07 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Martin Renner, Dec 11 2011
STATUS
approved