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A015124 Triangle of q-binomial coefficients for q=-11. 13


%S 1,1,1,1,-10,1,1,111,111,1,1,-1220,13542,-1220,1,1,13421,1637362,

%T 1637362,13421,1,1,-147630,198134223,-2177691460,198134223,-147630,1,

%U 1,1623931,23974093353,2898705467483,2898705467483,23974093353,1623931,1,1

%N Triangle of q-binomial coefficients for q=-11.

%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, A014993, A015262, A015279, A015300, A015317, A015334, A015353, A015368, A015383, A015499, A015418, A015434. - M. F. Hasler, Nov 04 & Nov 05 2012

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

%o (PARI) T015124(n, k, q=-11)=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), 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 GĂ©rard_

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Last modified January 23 19:36 EST 2020. Contains 331175 sequences. (Running on oeis4.)