A169794 Expansion of ((1-x)/(1-2*x))^7.
1, 7, 35, 147, 553, 1925, 6321, 19825, 59906, 175504, 500864, 1397536, 3823680, 10282496, 27230464, 71129856, 183518720, 468213760, 1182433280, 2958376960, 7338426368, 18059821056, 44120473600, 107055742976, 258122317824, 618683957248, 1474700509184
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Nickolas Hein, Jia Huang, Variations of the Catalan numbers from some nonassociative binary operations, arXiv:1807.04623 [math.CO], 2018.
- M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
- M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5.
- Index entries for linear recurrences with constant coefficients, signature (14, -84, 280, -560, 672, -448, 128).
Crossrefs
Programs
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Magma
m:=30; R
:=PowerSeriesRing(Integers(), m); Coefficients(R!(((1-x)/(1-2*x))^7)); // G. C. Greubel, Oct 16 2018 -
Maple
seq(coeff(series(((1-x)/(1-2*x))^7,x,n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Oct 16 2018
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Mathematica
CoefficientList[Series[((1 - x)/(1 - 2 x))^7, {x, 0, 26}], x] (* Michael De Vlieger, Oct 15 2018 *) -
PARI
x='x+O('x^30); Vec(((1-x)/(1-2*x))^7) \\ G. C. Greubel, Oct 16 2018
Formula
G.f.: ((1-x)/(1-2*x))^7.
For n > 0, a(n) = 2^(n-11)*(n+3)*(n+6)*(n^4 + 54*n^3 + 931*n^2 + 5454*n + 5080)/45. - Bruno Berselli, Aug 07 2011
Comments