login
A190050
Expansion of ((1-x)*(3*x^2-3*x+1))/(1-2*x)^3
3
1, 2, 6, 17, 46, 120, 304, 752, 1824, 4352, 10240, 23808, 54784, 124928, 282624, 634880, 1417216, 3145728, 6946816, 15269888, 33423360, 72876032, 158334976, 342884352, 740294656, 1593835520, 3422552064
OFFSET
0,2
COMMENTS
The second left hand column of triangle A175136.
FORMULA
G.f.: ((1-x)*(3*x^2-3*x+1))/(1-2*x)^3.
a(n) = (n^2 + 5*n + 10)*2^(n-4) for n >=1 with a(0)=1.
a(n) = A001788(n+1) -4*A001788(n) +6*A001788(n-1) -3*A001788(n-2) for n >=1 with a(0)=1.
MAPLE
A190050:= proc(n) option remember; if n=0 then A190050(n):=1: else A190050(n):=(n^2+5*n+10)*2^(n-4) fi: end: seq (A190050(n), n=0..26);
MATHEMATICA
Join[{1}, LinearRecurrence[{6, -12, 8}, {2, 6, 17}, 30]] (* or *) CoefficientList[Series[((1-x)*(3*x^2-3*x+1))/(1-2*x)^3, {x, 0, 50}], x] (* G. C. Greubel, Jan 10 2018 *)
PROG
(PARI) x='x+O('x^30); Vec(((1-x)*(3*x^2-3*x+1))/(1-2*x)^3) \\ G. C. Greubel, Jan 10 2018
(PARI) for(n=0, 30, print1(if(n==0, 1, (n^2 + 5*n + 10)*2^(n-4)), ", ")) \\ G. C. Greubel, Jan 10 2018
(Magma) [1] cat [(n^2 + 5*n + 10)*2^(n-4): n in [1..30]]; // G. C. Greubel, Jan 10 2018
CROSSREFS
Related to A001788.
Sequence in context: A350431 A316591 A222115 * A005592 A346169 A102403
KEYWORD
nonn,easy
AUTHOR
Johannes W. Meijer, May 06 2011
STATUS
approved