A052461 4-magic series constant.

1, 177, 5111, 60962, 430729, 2158099, 8488095, 27903044, 79895265, 205033333, 481386807, 1049954918, 2152397897, 4185095383, 7774354687, 13878462600, 23923217921, 39978597945, 64985300791, 103041066666, 159757914953

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Magic Constant.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

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

From G. C. Greubel, Sep 23 2019: (Start)

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

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)

Maple

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

Mathematica

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

Prog

(PARI) a(n)=(6*n^9+15*n^7+10*n^5-n)/30 \\ Charles R Greathouse IV, Jun 06 2013
(Magma) [n*(6*n^8 +15*n^6 +10*n^4 -1)/30: n in [1..25]]; // G. C. Greubel, Sep 23 2019
(Sage) [n*(6*n^8 +15*n^6 +10*n^4 -1)/30 for n in (1..25)] # G. C. Greubel, Sep 23 2019
(GAP) List([1..25], n-> n*(6*n^8 +15*n^6 +10*n^4 -1)/30); # G. C. Greubel, Sep 23 2019

Crossrefs

Cf. A052459, A052460.

Sequence in context: A292185 A083620 A097317 * A173375 A069398 A189910

Adjacent sequences: A052458 A052459 A052460 * A052462 A052463 A052464

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved