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Triangle of q-binomial coefficients for q=-12.
13

%I #8 Nov 05 2012 19:04:25

%S 1,1,1,1,-11,1,1,133,133,1,1,-1595,19285,-1595,1,1,19141,2775445,

%T 2775445,19141,1,1,-229691,399683221,-4793193515,399683221,-229691,1,

%U 1,2756293,57554154133,8283038077141,8283038077141,57554154133,2756293,1,1

%N Triangle of q-binomial coefficients for q=-12.

%C May be read as a symmetric triangular (T[n,k]=T[n,n-k]; k=0,...,n; n=0,1,...) or square array (A[n,r]=A[r,n]=T[n+r,r], read by antidiagonals). The diagonals of the former, or rows/columns of the latter, are, for k=0,...,12: A000012, A014994, A015264, A015281, A015302, A015319, A015336, A015354, A015369, A015384, A015401, A015421, A015436. - _M. F. Hasler_, Nov 04 2012

%H <a href="/index/Ga#Gaussian_binomial_coefficients">Index entries related to Gaussian binomial coefficients</a>.

%o (PARI) T015125(n, k, q=-12)=prod(i=1, k, (q^(1+n-i)-1)/(q^i-1)) \\ (Indexing is that of the triangular array: 0 <= k <= n = 0,1,2,...) - _M. F. Hasler_, Nov 04 2012

%Y Cf. analog triangles for other negative q=-2,...,-15: A015109 (q=-2), A015110 (q=-3), A015112 (q=-4), A015113 (q=-5), A015116 (q=-6), A015117 (q=-7), A015118 (q=-8), A015121 (q=-9), A015123 (q=-10), A015124 (q=-11), A015129 (q=-13), A015132 (q=-14), A015133 (q=-15). - _M. F. Hasler_, Nov 04 2012

%Y Cf. analog triangles for positive q=2,...,24: A022166 (q=2), A022167 (q=3), A022168, A022169, A022170, A022171, A022172, A022173, A022174 (q=10), A022175, A022176, A022177, A022178, A022179, A022180, A022181, A022182, A022183, A022184 (q=20), A022185, A022186, A022187, A022188. - _M. F. Hasler_, Nov 05 2012

%K sign,tabl,easy

%O 0,5

%A _Olivier GĂ©rard_