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 A202107 n^4*(n+1)^4/8. 0
 2, 162, 2592, 20000, 101250, 388962, 1229312, 3359232, 8201250, 18301250, 37949472, 74030112, 137149922, 243101250, 414720000, 684204032, 1095962562, 1710072162, 2606420000, 3889620000, 5694792642, 8194304162, 11605565952, 16200000000, 22313281250, 30356972802 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A relation between fourth powers and the sum of fifth and seventh powers. See the first formula, which is from Beiler. REFERENCES Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 161. LINKS Temple Rice Hollcroft, On sums of powers of n consecutive integers, Bulletin of the American Mathematical Society 59 (1953), nr. 6, p. 526 (574t). Index to sequences with linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1) FORMULA a(n) = 2*sum(k, k=1..n)^4 = sum(k^5 + k^7, k=1..n). a(n) = 2*A059977(n-1). a(n) = A000539(n) + A000541(n). G.f. -2*x*(1+72*x+603*x^2+1168*x^3+603*x^4+72*x^5+x^6) / (x-1)^9. - R. J. Mathar, Dec 13 2011 a(n) = 2*(A000217(n)^4). - Moshe Levin, Jan 21 2012 CROSSREFS Cf. A000217, A000539, A000541, A059977. Sequence in context: A179958 A178575 A069580 * A109420 A162904 A139928 Adjacent sequences:  A202104 A202105 A202106 * A202108 A202109 A202110 KEYWORD nonn,easy AUTHOR Martin Renner, Dec 11 2011 STATUS approved

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