A179838 Triangle T(n,k) read by rows: the coefficient [x^k] of the product_{s=1..n} (x+64*cos(s*Pi/(2n+1))^6), 0<=k<=n.
1, 1, 1, 1, 18, 1, 1, 129, 38, 1, 1, 571, 627, 58, 1, 1, 1884, 6212, 1525, 78, 1, 1, 5103, 43123, 24576, 2823, 98, 1, 1, 11998, 230241, 277500, 63660, 4521, 118, 1, 1, 25362, 1005267, 2379096, 1014681, 131464, 6619, 138, 1, 1, 49347, 3744753, 16359996, 12301986, 2724266, 235988, 9117, 158, 1
Offset: 0
Examples
1 1 1 1 18 1 1 129 38 1 1 571 627 58 1 1 1884 6212 1525 78 1 1 5103 43123 24576 2823 98 1 1 11998 230241 277500 63660 4521 118 1 1 25362 1005267 2379096 1014681 131464 6619 138 1 1 49347 3744753 16359996 12301986 2724266 235988 9117 158 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
- Alin Bostan, Bruno Salvy, Khang Tran, Generating functions of Chebyshev-like polynomials, 2009.
- Alin Bostan, Bruno Salvy, et al., Generating functions of Chebyshev-like polynomials, Intl. J. Number Theory 6 (7) (2010) 1659
Programs
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PARI
my(x='x+O('x^10)); concat(apply(p->Vecrev(p), Vec(Ser((1-x)*((x-1)^6 - t*x^2*(x+3)*(3*x+1))/(t^2*x^4-t*x*(x^4+14*x^3+34*x^2+14*x+1)*(x-1)^2+(x-1)^8))))) \\ Gheorghe Coserea, Apr 20 2017
Formula
A(x;t) = Sum_{n>=0} P_n(t)*x^n = (1-x)*((x-1)^6 - t*x^2*(x+3)*(3*x+1))/(t^2*x^4-t*x*(x^4+14*x^3+34*x^2+14*x+1)*(x-1)^2+(x-1)^8), where P_n(t) = Sum_{k=0..n} T(n,k)*t^k. - Gheorghe Coserea, Apr 20 2017
Extensions
Terms a(38) and beyond from Andrew Howroyd, Apr 13 2021
Comments