|
|
A081892
|
|
Second binomial transform of C(n+2,2).
|
|
4
|
|
|
1, 5, 22, 90, 351, 1323, 4860, 17496, 61965, 216513, 747954, 2558790, 8680203, 29229255, 97785144, 325241892, 1076168025, 3544180029, 11622614670, 37967207922, 123587135991, 400980206115, 1297083797172, 4184141281200
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Binomial transform of A049611(n+1).
2nd binomial transform of C(n+2,2), A000217.
3rd binomial transform of (1,2,1,0,0,0,.....)
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 3^(n - 2)*(n + 2)*(n + 9)/2 = 3^n*(n^2 + 11*n + 18)/18.
G.f.: (1 - 2*x)^2/(1 - 3*x)^3.
|
|
MATHEMATICA
|
LinearRecurrence[{9, -27, 27}, {1, 5, 22}, 50] (* G. C. Greubel, Oct 18 2018 *)
|
|
PROG
|
(PARI) x='x+O('x^30); Vec((1-2*x)^2/(1-3*x)^3) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^2/(1-3*x)^3)); // G. C. Greubel, Oct 18 2018
|
|
CROSSREFS
|
A right-edge column of triangle A024462.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|