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A015116 Triangle of q-binomial coefficients for q=-6. 13


%S 1,1,1,1,-5,1,1,31,31,1,1,-185,1147,-185,1,1,1111,41107,41107,1111,1,

%T 1,-6665,1480963,-8838005,1480963,-6665,1,1,39991,53308003,1910490043,

%U 1910490043,53308003,39991,1,1,-239945,1919128099,-412612541285

%N Triangle of q-binomial coefficients for q=-6.

%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 A000012 (k=0), A014987 (k=1), A015257 (k=2), A015273, A015292, A015310, A015328, A015345, A015361, A015378, A015392 (k=10), A015410, A015429,... - _M. F. Hasler_, Nov 04 2012

%t Table[QBinomial[n, k, -6], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Apr 09 2016 *)

%o (PARI) T015116(n, k, q=-6)=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), A015117 (q=-7), A015118 (q=-8), A015121 (q=-9), A015123 (q=-10), A015124 (q=-11), A015125 (q=-12), A015129 (q=-13), A015132 (q=-14), A015133 (q=-15); 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 04 2012

%K sign,tabl,easy

%O 0,5

%A _Olivier Gérard_

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Last modified January 21 21:30 EST 2020. Contains 331128 sequences. (Running on oeis4.)