A248619 a(n) = (n*(n+1))^4.

0, 16, 1296, 20736, 160000, 810000, 3111696, 9834496, 26873856, 65610000, 146410000, 303595776, 592240896, 1097199376, 1944810000, 3317760000, 5473632256, 8767700496, 13680577296, 20851360000, 31116960000, 45558341136, 65554433296, 92844527616, 129600000000

Offset: 0

Author

Eugene Chong, Oct 09 2014

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A016744, A059977; A002378: n*(n+1); A035287: n^2 *(n-1)^2; A060459: n^3*(n+1)^3.

Cf. A327773.

Programs

Magma

[(n*(n+1))^4: n in [0..30]]; // Vincenzo Librandi, Oct 16 2014

Maple

[ seq(n^4*(n+1)^4, n = 0..100) ];

Mathematica

Table[(n (n + 1))^4, {n, 0, 70}] (* or *) CoefficientList[Series[16 x (1 + 72 x + 603 x^2 + 1168 x^3 + 603 x^4 + 72 x^5 + x^6)/(1 - x)^9, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 16 2014 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,16,1296,20736,160000,810000,3111696,9834496,26873856},30] (* Harvey P. Dale, Sep 09 2016 *)

Formula

a(n) = A002378(n)^4 = A016744(A000217(n)).

a(n) = 16*A059977(n) for n>0.

G.f.: 16*x*(1 + 72*x + 603*x^2 + 1168*x^3 + 603*x^4 + 72*x^5 + x^6)/(1 - x)^9. - Vincenzo Librandi, Oct 16 2014

Sum_{n>=1} 1/a(n) = A327773 = -35 + 10*Pi^2/3 + Pi^4/45. - Vaclav Kotesovec, Sep 25 2019

Extensions

Terms a(76) and beyond corrected by Andrew Howroyd, Feb 20 2018