OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: A(x) = 16*x/(1-(1-2*x)^8).
EXAMPLE
A(x) = 1 + 7*x + 21*x^2 + 21*x^3 - 63*x^4 - 231*x^5 - 15*x^6 +-...
For n>=0, the first (n+1) coefficients of A(x)^(n+1) forms the
n-th row polynomial R_n(y) of triangle A097181:
A^1 = {1, _7, 21, 21, -63, -231, -15, 1521, ...}
A^2 = {1, 14, _91, 336, 609, -462, -5469, -9516, ...}
A^3 = {1, 21, 210, _1288, 5103, 11655, 2160, -85590, ...}
A^4 = {1, 28, 378, 3220, _18907, 77280, 199860, 153000, ...}
A^5 = {1, 35, 595, 6475, 49910, _283192, 1175190, 3282870, ...}
A^6 = {1, 42, 861, 11396, 108402, 778596, _4296034, 17959968, ...}
These row polynomials satisfy: R_n(1/2) = 8^n:
8^1 = 1 + 14/2;
8^2 = 1 + 21/2 + 210/2^2;
8^3 = 1 + 28/2 + 378/2^2 + 3220/2^3;
8^4 = 1 + 35/2 + 595/2^2 + 6475/2^3 + 49910/2^4.
MAPLE
seq(coeff(series(16*x/(1-(1-2*x)^8), x, n+2), x, n), n = 0..30); # G. C. Greubel, Sep 17 2019
MATHEMATICA
CoefficientList[Series[16*x/(1-(1-2*x)^8), {x, 0, 30}], x] (* G. C. Greubel, Sep 17 2019 *)
PROG
(PARI) a(n)=polcoeff(16*x/(1-(1-2*x)^8)+x*O(x^n), n, x)
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 16*x/(1-(1-2*x)^8) )); // G. C. Greubel, Sep 17 2019
(Sage)
def A097194_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P(16*x/(1-(1-2*x)^8)).list()
A097194_list(30) # G. C. Greubel, Sep 17 2019
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Aug 03 2004
STATUS
approved