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%I #16 Jun 17 2017 03:55:03
%S 0,720,665280,13366080,96909120,427518000,1402410240,3776965920,
%T 8835488640,18595558800,36045979200,65418312960,112492013760,
%U 184933148400,292666711680,448282533600,667474778880,969515038800,1377759015360,1920186797760,2629976731200
%N 6n*(6n-1)*(6n-2)*(6n-3)*(6n-4)*(6n-5).
%D R. Tijdeman, Some applications of Diophantine approximation, pp. 261-284 of Surveys in Number Theory (Urbana, May 21, 2000), ed. M. A. Bennett et al., Peters, 2003.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n)= A053625(6n)=(6n)!/(6(n-1))!.
%F Sum_{n>0} 1/a(n) = (192*log 2 - 81*log 3 - 7*Pi*sqrt 3)/4320 (cf. Tijdeman).
%F G.f.: -720*x*(462*x^5+9142*x^4+24017*x^3+12117*x^2+917*x+1) / (x-1)^7. - _Colin Barker_, Sep 13 2014
%t Table[Times@@(6n-Range[0,5]),{n,0,20}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,720,665280,13366080,96909120,427518000,1402410240},30] (* _Harvey P. Dale_, Nov 24 2015 *)
%o (PARI) concat(0, Vec(-720*x*(462*x^5+9142*x^4+24017*x^3+12117*x^2+917*x+1)/(x-1)^7 + O(x^100))) \\ _Colin Barker_, Sep 13 2014
%K easy,nonn
%O 0,2
%A _Henry Bottomley_, May 19 2000
%E More terms from _Colin Barker_, Sep 13 2014
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