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A015123 Triangle of q-binomial coefficients for q=-10. 13


%S 1,1,1,1,-9,1,1,91,91,1,1,-909,9191,-909,1,1,9091,918191,918191,9091,

%T 1,1,-90909,91828191,-917272809,91828191,-90909,1,1,909091,9182728191,

%U 917364637191,917364637191,9182728191,909091,1,1,-9090909,918273728191

%N Triangle of q-binomial coefficients for q=-10.

%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 in the former, or row/columns in the latter, are then (k=0,...,12): A000012, A014992, A015261, A015278, A015298, A015316, A015333, A015350, A015367, A015382, A015398, A015417, A015433. - _M. F. Hasler_, Nov 04 & Nov 05 2012

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

%t Table[QBinomial[n, k, -10], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Apr 09 2016 *)

%o (PARI) T015123(n, k, q=-10)=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 q: A015109 (q=-2), A015110 (q=-3), A015112 (q=-4), A015113 (q=-5), A015116 (q=-6), A015117 (q=-7), A015118 (q=-8), A015121 (q=-9), A015124 (q=-11), A015125 (q=-12), 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 Gérard_

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Last modified April 19 10:34 EDT 2019. Contains 322252 sequences. (Running on oeis4.)