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

0,2

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).

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

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 *)

Prog

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

Crossrefs

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

Cf. A327773.

Sequence in context: A016828 A072161 A173544 * A334585 A163929 A072914

Adjacent sequences: A248616 A248617 A248618 * A248620 A248621 A248622

Keyword

nonn,easy

Author

Eugene Chong, Oct 09 2014

Extensions

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

Status

approved