A015132 Triangle of (Gaussian) q-binomial coefficients for q=-14.

1, 1, 1, 1, -13, 1, 1, 183, 183, 1, 1, -2561, 36051, -2561, 1, 1, 35855, 7063435, 7063435, 35855, 1, 1, -501969, 1384469115, -19375002205, 1384469115, -501969, 1, 1, 7027567, 271355444571, 53166390519635, 53166390519635, 271355444571

Offset: 0

Author

Olivier Gérard

Keywords

• sign
• tabl
• easy

Comments

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). - M. F. Hasler, Nov 04 2012

Links

• Index entries related to Gaussian binomial coefficients.

Crossrefs

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), A015125 (q=-12), A015129 (q=-13), A015133 (q=-15). - M. F. Hasler, Nov 04 2012

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

Programs

PARI

T015132(n, k, q=-14)=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