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A202109 a(n) = n^3*(n+1)^3*(n+2)^3/72. 1
3, 192, 3000, 24000, 128625, 526848, 1778112, 5184000, 13476375, 31944000, 70180968, 144685632, 282589125, 526848000, 943296000, 1630015488, 2729559627, 4444632000, 7057911000, 10956792000, 16663911033, 24874409472, 36501000000, 52728000000, 75075609375 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 162.
LINKS
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.
a(n) = Sum_{k=1..n} A000217(k)^3+2*A000217(k)^4.
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
Sequence in context: A032594 A159658 A257038 * A230171 A332957 A203749
KEYWORD
nonn,easy
AUTHOR
Martin Renner, Dec 11 2011
STATUS
approved

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Last modified July 13 21:32 EDT 2024. Contains 374288 sequences. (Running on oeis4.)