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A274622 Irregular triangular array read by rows: coefficients in expansion of Gosper's q-sine function sin_q(Pi*z). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

Table of n, a(n) for n=0..79.

R. W. Gosper, Experiments and discoveries in q-trigonometry, Preprint.

R. W. Gosper, q-Trigonometry: Some Prefatory Afterthoughts

EXAMPLE

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,

...

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-Fran├žois Alcover, Oct 07 2016 *)

CROSSREFS

Cf. A274623, A274624, A274625.

Sequence in context: A099491 A322082 A334770 * A138189 A110090 A196831

Adjacent sequences:  A274619 A274620 A274621 * A274623 A274624 A274625

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Jul 04 2016

STATUS

approved

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Last modified June 24 02:11 EDT 2021. Contains 345408 sequences. (Running on oeis4.)