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A052460 3-magic series constant. 3
1, 50, 675, 4624, 21125, 73926, 214375, 540800, 1225449, 2550250, 4952651, 9082800, 15873325, 26622974, 43095375, 67634176, 103295825, 154001250, 224707699, 321602000, 452316501, 626168950, 854427575, 1150602624 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Magic Constant.

Index to sequences with linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

FORMULA

a(n) = n^3/4 * (n^2 + 1)^2.

G.f.: x*(1+42*x+303*x^2+568*x^3+303*x^4+42*x^5+x^6)/(1-x)^8 .

a(1)=1, a(2)=50, a(3)=675, a(4)=4624, a(5)=21125, a(6)=73926, a(7)=214375, a(8)=540800, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+ 56*a(n-5)- 28*a(n-6)+8*a(n-7)-a(n-8). - Harvey P. Dale, Aug 14 2013

MATHEMATICA

Table[n^3/4 (n^2+1)^2, {n, 30}] (* or *) LinearRecurrence[ {8, -28, 56, -70, 56, -28, 8, -1}, {1, 50, 675, 4624, 21125, 73926, 214375, 540800}, 30] (* Harvey P. Dale, Aug 14 2013 *)

CoefficientList[Series[(1 + 42 x + 303 x^2 + 568 x^3 + 303 x^4 + 42 x^5 + x^6) / (x - 1)^8, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 14 2013 *)

CROSSREFS

Cf. A052459, A052461.

Sequence in context: A231583 A156965 A240385 * A224168 A223859 A223982

Adjacent sequences:  A052457 A052458 A052459 * A052461 A052462 A052463

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified November 22 22:27 EST 2014. Contains 249835 sequences.