A052461 - OEIS

%I #19 Sep 08 2022 08:44:59

%S 1,177,5111,60962,430729,2158099,8488095,27903044,79895265,205033333,

%T 481386807,1049954918,2152397897,4185095383,7774354687,13878462600,

%U 23923217921,39978597945,64985300791,103041066666,159757914953

%N 4-magic series constant.

%H G. C. Greubel, <a href="/A052461/b052461.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MagicConstant.html">Magic Constant.</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F G.f.: x*(x^8 +167*x^7 +3386*x^6 +17697*x^5 +30074*x^4 +17697*x^3 +3386*x^2 +167*x +1)/(x-1)^10. - _Colin Barker_, Jun 06 2013

%F From _G. C. Greubel_, Sep 23 2019: (Start)

%F a(n) = n*(6*n^8 +15*n^6 +10*n^4 -1)/30.

%F E.g.f.: x*(30 +2625*x +22915*x^2 +51970*x^3 +43816*x^4 +16191*x^5 +2787* x^6 +216*x^7 +6*x^8)*exp(x)/30. (End)

%p seq(n*(6*n^8 +15*n^6 +10*n^4 -1)/30, n=1..25); # _G. C. Greubel_, Sep 23 2019

%t Table[n*(6*n^8 +15*n^6 +10*n^4 -1)/30, {n, 25}] (* _G. C. Greubel_, Sep 23 2019 *)

%o (PARI) a(n)=(6*n^9+15*n^7+10*n^5-n)/30 \\ _Charles R Greathouse IV_, Jun 06 2013

%o (Magma) [n*(6*n^8 +15*n^6 +10*n^4 -1)/30: n in [1..25]]; // _G. C. Greubel_, Sep 23 2019

%o (Sage) [n*(6*n^8 +15*n^6 +10*n^4 -1)/30 for n in (1..25)] # _G. C. Greubel_, Sep 23 2019

%o (GAP) List([1..25], n-> n*(6*n^8 +15*n^6 +10*n^4 -1)/30); # _G. C. Greubel_, Sep 23 2019

%Y Cf. A052459, A052460.

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_