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A270369 Expansion of (1-7*x)/(1-9*x). 3
1, 2, 18, 162, 1458, 13122, 118098, 1062882, 9565938, 86093442, 774840978, 6973568802, 62762119218, 564859072962, 5083731656658, 45753584909922, 411782264189298, 3706040377703682, 33354363399333138, 300189270593998242, 2701703435345984178 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: (1-7*x)/(1-9*x).
a(n) = 9*a(n-1) for n>1.
a(n) = 2*9^(n-1) for n>0.
From Amiram Eldar, May 08 2023: (Start)
Sum_{n>=0} 1/a(n) = 25/16.
Sum_{n>=0} (-1)^n/a(n) = 11/20.
Product_{n>=1} (1 - 1/a(n)) = A132025. (End)
MATHEMATICA
CoefficientList[Series[(1-7x)/(1-9x), {x, 0, 20}], x] (* or *) Join[ {1}, NestList[9#&, 2, 20]] (* Harvey P. Dale, Oct 15 2017 *)
PROG
(PARI) Vec((1-7*x)/(1-9*x) + O(x^30))
CROSSREFS
Cf. A001019 (powers of 9), A054879 (partial sums), A132025.
Cf. similar sequences with g.f. (1-k*x)/(1-9*x) and k=0..8: A001019 (k=0; k=8 gives two initial 1's ), A055275 (k=1), A270472 (k=2), A092810 (k=3), A067403 (k=4), A270473 (k=5), A102518 (k=6), this sequence (k=7).
Sequence in context: A121933 A108550 A322282 * A352654 A144513 A037518
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 18 2016
STATUS
approved

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Last modified February 27 21:03 EST 2024. Contains 370378 sequences. (Running on oeis4.)