|
|
A074742
|
|
a(n) = (n^3 + 6n^2 - n + 12)/6.
|
|
3
|
|
|
2, 3, 7, 15, 28, 47, 73, 107, 150, 203, 267, 343, 432, 535, 653, 787, 938, 1107, 1295, 1503, 1732, 1983, 2257, 2555, 2878, 3227, 3603, 4007, 4440, 4903, 5397, 5923, 6482, 7075, 7703, 8367, 9068, 9807, 10585, 11403, 12262, 13163, 14107, 15095, 16128, 17207, 18333
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
REFERENCES
|
A. Schultze, Advanced Algebra, Macmillan, London, 1910; p. 552.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (2 - 5*x + 7*x^2 - 3*x^3)/(1-x)^4.
E.g.f.: exp(x)*(12 + 6*x + 9*x^2 + x^3)/6. - Stefano Spezia, Jul 12 2023
|
|
MATHEMATICA
|
Table[(n^3 + 6n^2 - n + 12)/6, {n, 0, 49}] (* Alonso del Arte, Jan 13 2012 *)
CoefficientList[Series[(2-5x+7x^2-3x^3)/(1-x)^4, {x, 0, 50}], x] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {2, 3, 7, 15}, 50] (* Harvey P. Dale, Aug 05 2022 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|