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A255183 Third differences of ninth powers (A001017).

%I A255183 #24 Sep 08 2022 08:46:11
%S A255183 1,509,18150,204630,1225230,4985070,15717750,41436870,95750430,
%T A255183 200038110,385991430,698516790,1199001390,1968942030,3113936790,
%U A255183 4768039590,7098477630,10310731710,14653979430,20426901270
%N A255183 Third differences of ninth powers (A001017).
%H A255183 Luciano Ancora, <a href="/A255183/b255183.txt">Table of n, a(n) for n = 0..1000</a>
%H A255183 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A255183 G.f.: (1 + 502*x + 14608*x^2 + 88234*x^3 + 156190*x^4 + 88234*x^5 + 14608*x^6 + 502*x^7 + x^8)/(1 - x)^7.
%F A255183 a(n) = 6*(84*n^6 - 252*n^5 + 630*n^4 - 840*n^3 + 756*n^2 - 378*n + 85) for n>1, a(0)=1, a(1)=509.
%e A255183 Third differences:   1, 509, 18150, 204630, 1225230, ...  (this sequence)
%e A255183 Second differences:  1, 510, 18660, 223290, 1448520, ...  (A255179)
%e A255183 First differences:   1, 511, 19171, 242461, 1690981, ...  (A022525)
%e A255183 ---------------------------------------------------------------------
%e A255183 The ninth powers:    1, 512, 19683, 262144, 1953125, ...  (A001017)
%e A255183 ---------------------------------------------------------------------
%t A255183 Join[{1, 509}, Table[6 (84 n^6 - 252 n^5 + 630 n^4 - 840 n^3 + 756 n^2 - 378 n + 85), {n, 2, 30}]]
%t A255183 Join[{1,509},Differences[Range[0,20]^9,3]] (* _Harvey P. Dale_, Apr 24 2015 *)
%o A255183 (Magma) [1,509] cat [6*(84*n^6-252*n^5+630*n^4-840*n^3+756*n^2-378*n+85): n in [2..30]]; // _Vincenzo Librandi_, Mar 18 2015
%Y A255183 Cf. A001017, A007487, A022525, A253637, A255179, A255182.
%K A255183 nonn,easy
%O A255183 0,2
%A A255183 _Luciano Ancora_, Mar 18 2015
%E A255183 Edited by _Bruno Berselli_, Mar 20 2015