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A241204
Expansion of (1 + 2*x)^2/(1 - 2*x)^2.
4
1, 8, 32, 96, 256, 640, 1536, 3584, 8192, 18432, 40960, 90112, 196608, 425984, 917504, 1966080, 4194304, 8912896, 18874368, 39845888, 83886080, 176160768, 369098752, 771751936, 1610612736, 3355443200, 6979321856, 14495514624, 30064771072, 62277025792
OFFSET
0,2
LINKS
FORMULA
a(n) = 2^(2+n)*n for n>0. - Colin Barker, Apr 23 2014
a(n) = 4*a(n-1)-4*a(n-2) for n>2. - Colin Barker, Apr 23 2014
From Amiram Eldar, Jan 13 2021: (Start)
Sum_{n>=1} 1/a(n) = log(2)/4.
Sum_{n>=1} (-1)^(n+1)/a(n) = log(3/2)/4. (End)
E.g.f.: 1 + 8*x*exp(x). - G. C. Greubel, Jun 07 2023
MAPLE
A241204:= n->`if`(n=0, 1, 2^(n+2)*n); seq(A241204(n), n=0..20); # Wesley Ivan Hurt, Apr 22 2014
MATHEMATICA
Table[2^(n+2)*n + Boole[n==0], {n, 0, 40}] (* G. C. Greubel, Jun 07 2023 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 41); Coefficients(R!((1+2*x)^2/(1-2*x)^2));
(PARI) Vec((2*x+1)^2/(2*x-1)^2 + O(x^100)) \\ Colin Barker, Apr 22 2014
(Sage)
def A241204(i):
if i==0: return 1
else: return 2^(2+i)*i;
[A241204(n) for n in (0..30)] # Bruno Berselli, Apr 23 2014
CROSSREFS
Subsequence of A008574.
Sequence in context: A286399 A014969 A139820 * A195590 A373867 A071345
KEYWORD
nonn,easy
AUTHOR
STATUS
approved