%I #30 Sep 08 2022 08:46:11

%S 1,125,1806,10206,35406,92526,201726,388206,682206,1119006,1738926,

%T 2587326,3714606,5176206,7032606,9349326,12196926,15651006,19792206,

%U 24706206,30483726,37220526,45017406,53980206,64219806,75852126,88998126,103783806,120340206

%N Third differences of seventh powers (A001015).

%H Lucuano Ancora, <a href="/A255181/b255181.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: (1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6)/(1 - x)^5.

%F a(n) = 42*(3 - 10*n + 15*n^2 - 10*n^3 + 5*n^4) for n>1, a(0)=1, a(1)=125.

%F a(n) = A255177(n)-A255177(n-1). - _R. J. Mathar_, Jul 16 2015

%e Third differences: 1, 125, 1806, 10206, 35406, ... (this sequence)

%e Second differences: 1, 126, 1932, 12138, 47544, ... (A255177)

%e First differences: 1, 127, 2059, 14197, 61741, ... (A022523)

%e ---------------------------------------------------------------------

%e The seventh powers: 1, 128, 2187, 16384, 78125, ... (A001015)

%e ---------------------------------------------------------------------

%t Join[{1, 125}, Table[42 (3 - 10 n + 15 n^2 - 10 n^3 + 5 n^4), {n, 2, 30}]]

%o (Magma) [1,125] cat [42*(3-10*n+15*n^2-10*n^3+5*n^4): n in [2..30]]; // _Vincenzo Librandi_, Mar 18 2015

%Y Cf. A000541, A001015, A022523, A255177.

%K nonn,easy

%O 0,2

%A _Luciano Ancora_, Mar 18 2015

%E Edited by _Bruno Berselli_, Mar 19 2015