A245380 (7*n^5+5*n^3)/12.

0, 1, 22, 153, 624, 1875, 4626, 9947, 19328, 34749, 58750, 94501, 145872, 217503, 314874, 444375, 613376, 830297, 1104678, 1447249, 1870000, 2386251, 3010722, 3759603, 4650624, 5703125, 6938126, 8378397, 10048528, 11974999, 14186250, 16712751, 19587072

Offset: 0

Author

Vincenzo Librandi, Jul 20 2014

Keywords

• nonn
• easy

Comments

7*n^5+5*n^3 = 0 (mod.12) for all n.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Programs

Magma

[(7*n^5+5*n^3)/12: n in [0..40]];

Mathematica

 Table[(7 n^5 + 5 n^3)/12, {n, 0, 40}] (* or *) CoefficientList[Series[x (x^4 + 16 x^3 + 36 x^2 + 16 x + 1)/(x - 1)^6, {x, 0, 40}], x]
LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,22,153,624,1875},40] (* Harvey P. Dale, Jan 20 2025 *)

Formula

G.f.: x*(x^4 + 16*x^3 + 36*x^2 + 16*x + 1)/(x - 1)^6.