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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, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Polynomial coefficients of H_n^(3)(x) by Bostan et al.

LINKS

Table of n, a(n) for n=0..37.

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

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

EXAMPLE

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

PROG

(PARI)

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

CROSSREFS

Cf. A179837.

Sequence in context: A203004 A155497 A202677 * A174678 A167884 A022181

Adjacent sequences:  A179835 A179836 A179837 * A179839 A179840 A179841

KEYWORD

tabl,nonn

AUTHOR

R. J. Mathar, Jan 10 2011

STATUS

approved

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Last modified February 19 10:34 EST 2019. Contains 320310 sequences. (Running on oeis4.)