|
|
A290061
|
|
a(n) = (1/24)*(n + 3)*(3*n^3 + 5*n^2 - 6*n + 16).
|
|
3
|
|
|
3, 10, 31, 77, 162, 303, 520, 836, 1277, 1872, 2653, 3655, 4916, 6477, 8382, 10678, 13415, 16646, 20427, 24817, 29878, 35675, 42276, 49752, 58177, 67628, 78185, 89931, 102952, 117337, 133178, 150570, 169611, 190402, 213047, 237653, 264330, 293191, 324352, 357932
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(3 - 5*x + 11*x^2 - 8*x^3 + 2*x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4.
(End)
|
|
MATHEMATICA
|
Table[(1/24)(n+3)(3n^3+5n^2-6n+16), {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {3, 10, 31, 77, 162}, 40] (* Harvey P. Dale, Oct 29 2018 *)
|
|
PROG
|
(PARI) Vec(x*(3 - 5*x + 11*x^2 - 8*x^3 + 2*x^4) / (1 - x)^5 + O(x^50)) \\ Colin Barker, Jul 20 2017
(PARI) vector(50, n, (n+3)*(3*n^3+5*n^2-6*n+16)/24) \\ Derek Orr, Jul 24 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|