cp's OEIS Frontend

A255179 Second differences of ninth powers (A001017).

%I A255179 #58 Feb 21 2023 02:21:41
%S A255179 1,510,18660,223290,1448520,6433590,22151340,63588210,159338640,
%T A255179 359376750,745368180,1443884970,2642886360,4611828390,7725765180,
%U A255179 12493804770,19592282400,29903014110,44556993540,64983894810,92967744360,130709124630,180894272460
%N A255179 Second differences of ninth powers (A001017).
%H A255179 Luciano Ancora, <a href="/A255179/b255179.txt">Table of n, a(n) for n = 0..1000</a>
%H A255179 Luciano Ancora, <a href="https://issuu.com/quadernite/docs/libro01">Sums of powers of positive integers and their recurrence relations</a>, section 0.5.
%H A255179 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A255179 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)^8.
%F A255179 a(n) = 6*n*(3 + 28*n^2 + 42*n^4 + 12*n^6) for n>0, a(0)=1.
%e A255179 Second differences:  1, 510, 18660, 223290, 1448520, ... (this sequence)
%e A255179 First differences:   1, 511, 19171, 242461, 1690981, ... (A022525)
%e A255179 ------------------------------------------------------------------------
%e A255179 The ninth powers:    1, 512, 19683, 262144, 1953125, ... (A001017)
%e A255179 ------------------------------------------------------------------------
%e A255179 First partial sums:  1, 513, 20196, 282340, 2235465, ... (A007487)
%e A255179 Second partial sums: 1, 514, 20710, 303050, 2538515, ... (A253637)
%e A255179 Third partial sums:  1, 515, 21225, 324275, 2862790, ... (A254643)
%t A255179 Join[{1}, Table[6 n (3 + 28 n^2 + 42 n^4 + 12 n^6), {n, 1, 30}]]
%t A255179 Join[{1},Differences[Range[0,30]^9,2]] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,510,18660,223290,1448520,6433590,22151340,63588210,159338640},30] (* _Harvey P. Dale_, Jan 26 2019 *)
%o A255179 (Magma) [1] cat [6*n*(3+28*n^2+42*n^4+12*n^6): n in [1..30]]; // _Vincenzo Librandi_, Mar 12 2015
%Y A255179 Cf. A001017, A007487, A022525, A253637, A254643, A255177, A255178.
%K A255179 nonn,easy
%O A255179 0,2
%A A255179 _Luciano Ancora_, Feb 21 2015
%E A255179 Corrected g.f. by _Bruno Berselli_, Feb 25 2015
%E A255179 Offset changed by _Bruno Berselli_, Mar 20 2015