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%I #53 Sep 08 2022 08:46:13
%S 1,123,1557,6719,16800,31920,52080,77280,107520,142800,183120,228480,
%T 278880,334320,394800,460320,530880,606480,687120,772800,863520,
%U 959280,1060080,1165920,1276800,1392720,1513680,1639680,1770720,1906800,2047920,2194080,2345280,2501520,2662800
%N Fifth differences of 7th powers (A001015).
%D John H. Conway and Richard K. Guy, The Book of Numbers. New York: Springer-Verlag, pp. 30-32, 1996.
%D Kiran Parulekar. Amazing Properties of Squares and Their Calculations. Kiran Anil Parulekar, 2012.
%D Bag, Amulya Kumar (1966). "Binomial theorem in ancient India". Indian J. History Sci 1 (1): 68-74.
%D Ronald Graham and Donald Knuth, Patashnik, Oren (1994). "(5) Binomial Coefficients". Concrete Mathematics (2nd ed.). Addison Wesley. pp. 153-256.
%H R. J. Mathar, <a href="/A259907/b259907.txt">Table of n, a(n) for n = 0..79</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: (1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6)/(1 - x)^3.
%F a(n) = 840*(3*n^2 - 9*n + 8) for n>3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6. - _Vincenzo Librandi_, Jul 08 2015
%e 1 128 2187 16384 78125 279936 823543 2097152 4782969 (seventh powers)
%e 1 127 2059 14197 61741 201811 543607 1273609 2685817 (first differences)
%e 1 126 1932 12138 47544 140070 341796 730002 1412208 (second differences)
%e 1 125 1806 10206 35406 92526 201726 388206 682206 (third differences)
%e 1 124 1681 8400 25200 57120 109200 186480 294000 (fourth differences)
%e 1 123 1557 6719 16800 31920 52080 77280 107520 (here)
%t Join[{1, 123, 1557, 6719}, Table[840 (3 n^2 - 9 n + 8), {n, 4, 40}]]
%o (Sage) [1,123,1557,6719]+[840*(3*n^2-9*n+8) for n in (4..40)] # _Bruno Berselli_, Jul 16 2015
%o (Magma) [1,123,1557,6719] cat [840*(3*n^2-9*n+8): n in [4..40]]; // _Bruno Berselli_, Jul 16 2015
%Y Cf. A001015, A022523, A255177, A255181.
%K nonn,easy
%O 0,2
%A _Kolosov Petro_, Jul 07 2015
%E Edited by Editors of the OEIS, Jul 16 2015
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