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 A255177 Second differences of seventh powers (A001015). 7
 1, 126, 1932, 12138, 47544, 140070, 341796, 730002, 1412208, 2531214, 4270140, 6857466, 10572072, 15748278, 22780884, 32130210, 44327136, 59978142, 79770348, 104476554, 134960280, 172180806, 217198212, 271178418 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Luciano Ancora, Table of n, a(n) for n = 0..1000 Luciano Ancora, Sums of powers of positive integers and their recurrence relations, section 0.5. Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA G.f.: (1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6)/(1 - x)^6. a(n) = 14*n*(3*n^4 + 5*n^2 + 1) for n>0, a(0)=1. a(n) = A022523(n)-A022523(n-1). - R. J. Mathar, Jul 16 2015 EXAMPLE Second differences:  1, 126, 1932, 12138,  47544, ... (this sequence) First differences:   1, 127, 2060, 14324,  63801, ... (A152726) ---------------------------------------------------------------------- The seventh powers:  1, 128, 2187, 16384,  78125, ... (A001015) ---------------------------------------------------------------------- First partial sums:  1, 129, 2316, 18700,  96825, ... (A000541) Second partial sums: 1, 130, 2446, 21146, 117971, ... (A250212) Third partial sums:  1, 131, 2577, 23723, 141694, ... (A254641) Fourth partial sums: 1, 132, 2709, 26432, 168126, ... (A254646) Fifth partial sums:  1, 133, 2842, 29274, 197400, ... (A254684) MATHEMATICA Join[{1}, Table[14 n (3 n^4 + 5 n^2 + 1), {n, 1, 30}], {n, 0, 24}] (* or *) CoefficientList[Series[(1 + 120 x + 1191 x^2 + 2416 x^3 + 1191 x^4 + 120 x^5 + x^6)/(1 - x)^6, {x, 0, 22}], x] PROG (MAGMA) [1] cat [14*(-1+n)*(9-22*n+23*n^2-12*n^3+3*n^4): n in [2..30]]; // Vincenzo Librandi, Mar 12 2015 CROSSREFS Cf. A000541, A001015, A152726, A250212, A254641, A254646, A254684, A255178, A255179. Sequence in context: A267628 A304559 A189345 * A172140 A196414 A133499 Adjacent sequences:  A255174 A255175 A255176 * A255178 A255179 A255180 KEYWORD nonn,easy AUTHOR Luciano Ancora, Feb 21 2015 EXTENSIONS Edited by Bruno Berselli, Mar 19 2015 STATUS approved

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Last modified October 15 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)