A179837 Triangle T(n,k) read by rows: the coefficient [x^k] of the product_{s=1..n} (x+16*cos(s*Pi/(2n+1))^4), 0<=k<=n.

1, 1, 1, 1, 7, 1, 1, 26, 13, 1, 1, 70, 87, 19, 1, 1, 155, 403, 184, 25, 1, 1, 301, 1462, 1216, 317, 31, 1, 1, 532, 4446, 6190, 2725, 486, 37, 1, 1, 876, 11826, 25954, 17903, 5146, 691, 43, 1, 1, 1365, 28314, 93536, 96055, 41461, 8695, 932, 49, 1, 1, 2035

Offset

0,5

Comments

Polynomial coefficients of H_n^(2)(x) by Bostan et al.

Links

Table of n, a(n) for n=0..56.

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

T(n,1) = A006325(n+1).

A(x;t) = Sum_{n>=0} P_n(t)*x^n = (1-x)^3/((x-1)^4 - t*x*(x+1)^2), where P_n(t) = Sum_{k=0..n} T(n,k)*t^k. - Gheorghe Coserea, Apr 20 2017

Example

1
1 1
1 7 1
1 26 13 1
1 70 87 19 1
1 155 403 184 25 1
1 301 1462 1216 317 31 1
1 532 4446 6190 2725 486 37 1
1 876 11826 25954 17903 5146 691 43 1
1 1365 28314 93536 96055 41461 8695 932 49 1
1 2035 62271 298376 439019 271467 83020 13588 1209 55 1

Prog

(PARI)
x='x+O('x^11); concat(apply(p->Vecrev(p), Vec(Ser((1-x)^3/((x-1)^4 - t*x*(x+1)^2))))) \\ Gheorghe Coserea, Apr 20 2017

Crossrefs

Cf. A179838

Sequence in context: A053714 A168290 A218695 * A238743 A168517 A142465

Adjacent sequences: A179834 A179835 A179836 * A179838 A179839 A179840

Keyword

tabl,nonn

Author

R. J. Mathar, Jan 10 2011

Status

approved