A015113 Triangle of q-binomial coefficients for q=-5.

1, 1, 1, 1, -4, 1, 1, 21, 21, 1, 1, -104, 546, -104, 1, 1, 521, 13546, 13546, 521, 1, 1, -2604, 339171, -1679704, 339171, -2604, 1, 1, 13021, 8476671, 210302171, 210302171, 8476671, 13021, 1, 1, -65104, 211929796, -26279294704, 131649159046

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). The diagonals of the former (or rows/columns of the latter) are A000012 (k=0), A014986 (k=1), A015255 (k=2), A015272, A015291, A015309, A015327, A015344, A015360, A015377, A015391 (k=10), A015409, A015427,... - M. F. Hasler, Nov 04 2012

Crossrefs

Cf. analog triangles for other q: A015109 (q=-2), A015110 (q=-3), A015112 (q=-4), A015116 (q=-6), 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

Programs

Mathematica

Table[QBinomial[n, k, -5], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 09 2016 *)

PARI

T015113(n, k, q=-5)=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