A015112 Triangle of q-binomial coefficients for q=-4.

1, 1, 1, 1, -3, 1, 1, 13, 13, 1, 1, -51, 221, -51, 1, 1, 205, 3485, 3485, 205, 1, 1, -819, 55965, -219555, 55965, -819, 1, 1, 3277, 894621, 14107485, 14107485, 894621, 3277, 1, 1, -13107, 14317213, -901984419, 3625623645, -901984419, 14317213, -13107, 1, 1

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), A014985 (k=1), A015253 (k=2), A015271, A015289, A015308, A015326, A015341, A015359, A015376, A015390 (k=10), A015408, A015425,... - M. F. Hasler, Nov 04 2012

Crossrefs

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

Flatten[Table[QBinomial[n,m,-4],{n,0,10},{m,0,n}]] (* Harvey P. Dale, Jun 10 2015 *)

PARI

T015112(n, k, q=-4)=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