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%I #37 Sep 08 2022 08:46:10
%S 0,16,1296,20736,160000,810000,3111696,9834496,26873856,65610000,
%T 146410000,303595776,592240896,1097199376,1944810000,3317760000,
%U 5473632256,8767700496,13680577296,20851360000,31116960000,45558341136,65554433296,92844527616,129600000000
%N a(n) = (n*(n+1))^4.
%H Andrew Howroyd, <a href="/A248619/b248619.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F a(n) = A002378(n)^4 = A016744(A000217(n)).
%F a(n) = 16*A059977(n) for n>0.
%F G.f.: 16*x*(1 + 72*x + 603*x^2 + 1168*x^3 + 603*x^4 + 72*x^5 + x^6)/(1 - x)^9. - _Vincenzo Librandi_, Oct 16 2014
%F Sum_{n>=1} 1/a(n) = A327773 = -35 + 10*Pi^2/3 + Pi^4/45. - _Vaclav Kotesovec_, Sep 25 2019
%p [ seq(n^4*(n+1)^4, n = 0..100) ];
%t Table[(n (n + 1))^4, {n, 0, 70}] (* or *) CoefficientList[Series[16 x (1 + 72 x + 603 x^2 + 1168 x^3 + 603 x^4 + 72 x^5 + x^6)/(1 - x)^9, {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 16 2014 *)
%t LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,16,1296,20736,160000,810000,3111696,9834496,26873856},30] (* _Harvey P. Dale_, Sep 09 2016 *)
%o (Magma) [(n*(n+1))^4: n in [0..30]]; // _Vincenzo Librandi_, Oct 16 2014
%Y Cf. A016744, A059977; A002378: n*(n+1); A035287: n^2 *(n-1)^2; A060459: n^3*(n+1)^3.
%Y Cf. A327773.
%K nonn,easy
%O 0,2
%A _Eugene Chong_, Oct 09 2014
%E Terms a(76) and beyond corrected by _Andrew Howroyd_, Feb 20 2018
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