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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
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OFFSET
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1,1
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COMMENTS
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A relation between fourth powers and the sum of fifth and seventh powers. See the first formula, which is from Beiler.
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REFERENCES
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Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 161.
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LINKS
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Table of n, a(n) for n=1..26.
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)
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FORMULA
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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
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CROSSREFS
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Cf. A000217, A000539, A000541, A059977.
Sequence in context: A179958 A178575 A069580 * A109420 A162904 A139928
Adjacent sequences: A202104 A202105 A202106 * A202108 A202109 A202110
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KEYWORD
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nonn,easy
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AUTHOR
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Martin Renner, Dec 11 2011
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STATUS
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approved
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