A163277 a(n) = n^7*(n+1)^2/2.

0, 2, 576, 17496, 204800, 1406250, 6858432, 26353376, 84934656, 239148450, 605000000, 1403076312, 3027787776, 6149354666, 11859019200, 21870000000, 38788923392, 66474865026, 110505715776, 178774347800, 282240000000

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

From R. J. Mathar, Feb 05 2010: (Start)

a(n) = n^2*A163275(n).

G.f.: 2*x*(1 +278*x +5913*x^2 +27760*x^3 +38435*x^4 +16434*x^5 +1867*x^6 +32*x^7)/(x-1)^10. (End)

From Amiram Eldar, May 14 2022: (Start)

Sum_{n>=1} 1/a(n) = 16 - 7*Pi^2/3 - 4*Pi^4/45 - 4*Pi^6/945 + 10*zeta(3) + 6*zeta(5) + 2*zeta(7).

Sum_{n>=1} (-1)^(n+1)/a(n) = 28*log(2) + 15*zeta(3)/2 + 45*zeta(5)/8 + 63*zeta(7)/32 - 16 - 5*Pi^2/6 - 7*Pi^4/90 - 31*Pi^6/7560. (End)

Maple

A163277 := proc(n) n^7*(n+1)^2/2 ; end proc: seq(A163277(n), n=0..60) ; \\ R. J. Mathar, Feb 05 2010

Mathematica

Table[(1/2)*n^7*(n + 1)^2, {n, 0, 50}] (* G. C. Greubel, Dec 12 2016 *)

Prog

(PARI) concat([0], Vec(2*x*(1 +278*x +5913*x^2 +27760*x^3 +38435*x^4 +16434*x^5 +1867*x^6 +32*x^7)/(x-1)^10 + O(x^50))) \\ G. C. Greubel, Dec 12 2016
(Magma) [n^7*(n+1)^2/2: n in [0..30]]; // Vincenzo Librandi, Dec 13 2016

Crossrefs

Cf. A006002, A099903, A163102, A163274, A163275, A163276.

Sequence in context: A049364 A159529 A195001 * A003830 A134371 A306635

Adjacent sequences: A163274 A163275 A163276 * A163278 A163279 A163280

Keyword

easy,nonn

Author

Omar E. Pol, Jul 24 2009

Extensions

Extended by R. J. Mathar, Feb 05 2010

Status

approved