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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 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. 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 Cf. A000217, A000292, A002117. Sequence in context: A032594 A159658 A257038 * A230171 A332957 A203749 Adjacent sequences: A202106 A202107 A202108 * A202110 A202111 A202112 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.)