A054779 6n*(6n-1)*(6n-2)*(6n-3)*(6n-4)*(6n-5).

0, 720, 665280, 13366080, 96909120, 427518000, 1402410240, 3776965920, 8835488640, 18595558800, 36045979200, 65418312960, 112492013760, 184933148400, 292666711680, 448282533600, 667474778880, 969515038800, 1377759015360, 1920186797760, 2629976731200

Offset: 0

Author

Henry Bottomley, May 19 2000

Keywords

• easy
• nonn

References

• 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.

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Programs

Mathematica

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 *)

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

Formula

a(n)= A053625(6n)=(6n)!/(6(n-1))!.

Sum_{n>0} 1/a(n) = (192*log 2 - 81*log 3 - 7*Pi*sqrt 3)/4320 (cf. Tijdeman).

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

Extensions

More terms from Colin Barker, Sep 13 2014