A274622 Irregular triangular array read by rows: coefficients in expansion of Gosper's q-sine function sin_q(Pi*z).

1, 1, 2, 2, 1, 4, 4, 1, 2, 8, 8, 2, 4, 14, 14, 4, 8, 24, 24, 8, 1, 14, 40, 40, 14, 1, 2, 24, 64, 64, 24, 2, 4, 40, 100, 100, 40, 4, 8, 64, 154, 154, 64, 8, 14, 100, 232, 232, 100, 14, 24, 154, 344, 344, 154, 24, 1, 40, 232, 504, 504, 232, 40, 1, 2, 64, 344, 728, 728, 344, 64, 2, 4, 100, 504, 1040, 1040, 504, 100, 4

Offset: 0

Author

N. J. A. Sloane, Jul 04 2016

Keywords

• nonn
• tabf

Examples

			The array begins:
.........1,1,
.........2,2,
.......1,4,4,1,
.......2,8,8,2,
.......4,14,14,4,
.......8,24,24,8,
....1,14,40,40,14,1,
....2,24,64,64,24,2,
....4,40,100,100,40,4,
....8,64,154,154,64,8,
....14,100,232,232,100,14,
....24,154,344,344,154,24,
..1,40,232,504,504,232,40,1,
..2,64,344,728,728,344,64,2,
..4,100,504,1040,1040,504,100,4,
...
		

References

• R. W. Gosper, Experiments and discoveries in q-trigonometry, in Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics. Editors: F. G. Garvan and M. E. H. Ismail. Kluwer, Dordrecht, Netherlands, 2001, pp. 79-105.

Links

• R. W. Gosper, Experiments and discoveries in q-trigonometry, Preprint.
• R. W. Gosper, q-Trigonometry: Some Prefatory Afterthoughts

Crossrefs

Cf. A274623, A274624, A274625.

Programs

Mathematica

nmax = 14; kmax = 4; QP = QPochhammer; s = QP[q^2]/QP[q]^2 + O[q]^(nmax + 1); col[1] = CoefficientList [s, q]; col[k_] := Join[Array[0&, k(k-1)], Take[col[1], nmax-k(k-1)+1]]; T = Transpose[Array[col, kmax]]; ro[n_] := DeleteCases[T[[n+1]], 0]; row[n_] := Join[Reverse[ro[n]], ro[n]]; Table[row[n], {n, 0, nmax}] // Flatten (* Jean-François Alcover, Oct 07 2016 *)