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n^3*(n^4 + n^2 - 1).
1

%I #16 Sep 08 2022 08:46:07

%S 1,152,2403,17344,81125,287496,840007,2129408,4841289,10099000,

%T 19646891,36078912,63117613,105948584,171615375,269479936,411753617,

%U 614103768,896340979,1283192000,1805163381,2499500872,3411249623,4594420224,6113265625,8043673976

%N n^3*(n^4 + n^2 - 1).

%C Row sums of A016755 read as triangular array.

%H Vincenzo Librandi, <a href="/A239065/b239065.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n^7 + n^5 - n^3.

%F G.f.: x*(1+144*x+1215*x^2+2320*x^3+1215*x^4+144*x^5+x^6)/(x-1)^8.

%e A016755, as triangular array begins:

%e 1;

%e 27, 125;

%e 343, 729, 1331;

%e 2197, 3375, 4913, 6859;

%e 9261, 12167, 15625, 19683, 24389;

%e 29791, 35937, 42875, 50653, 59319, 68921;..

%e Row sums are:

%e 1;

%e 3^3 + 5^3 = 27 + 125 = 152;

%e 7^3 + 9^3 + 11^3 = 343 + 729 + 1331 = 2403;

%e 13^3 + 15^3 + 17^3 + 19^3 = 2197 + 3375 + 4913 + 6859 = 17344;

%e 21^3 + 23^3 + 25^3 + 27^3 + 29^3 = 9261 + 12167 + 15625 + 19683 + 24389 = 81125;

%e 31^3 + 33^3 + 35^3 + 37^3 + 39^3 + 41^3 = 287496 = 66^3.

%p A239065:=n->n^7 + n^5 - n^3; seq(A239065(n), n=1..30); # _Wesley Ivan Hurt_, Mar 09 2014

%t Table[n^7 + n^5 - n^3, {n, 30}] (* _Wesley Ivan Hurt_, Mar 09 2014 *)

%t CoefficientList[Series[(1 + 144 x + 1215 x^2 + 2320 x^3 + 1215 x^4 + 144 x^5 + x^6)/(x - 1)^8, {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 11 2014 *)

%o (PARI) a(n) = n^7+n^5-n^3 \\ _Charles R Greathouse IV_, Mar 09 2014

%o (Magma) [n^3*(n^4 + n^2 - 1): n in [1..30]]; // _Vincenzo Librandi_, Mar 11 2014

%Y Cf. A016755.

%K easy,nonn

%O 1,2

%A _Philippe Deléham_, Mar 09 2014