A015118 Triangle of q-binomial coefficients for q=-8.

1, 1, 1, 1, -7, 1, 1, 57, 57, 1, 1, -455, 3705, -455, 1, 1, 3641, 236665, 236665, 3641, 1, 1, -29127, 15150201, -120935815, 15150201, -29127, 1, 1, 233017, 969583737, 61934287481, 61934287481, 969583737, 233017, 1, 1, -1864135, 62053592185

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), A014990 (k=1), A015259 (k=2), A015276 (k=3), A015294 (k=4), A015313 (k=5), A015331 (k=6), A015347 (k=7), A015364 (k=8), A015380 (k=9), A015394 (k=10), A015413 (k=11), A015431 (k=12). - M. F. Hasler, Nov 04 2012

Links

• Index entries related to Gaussian binomial coefficients.

Crossrefs

Cf. analog triangles for negative q=-2,...,-15: A015109 (q=-2), A015110 (q=-3), A015112 (q=-4), A015113 (q=-5), A015116 (q=-6), A015117 (q=-7), A015121 (q=-9), A015123 (q=-10), A015124 (q=-11), A015125 (q=-12), A015129 (q=-13), A015132 (q=-14), 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

Mathematica

Table[QBinomial[n, k, -8], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 09 2016 *)

PARI

T015118(n, k, q=-8)=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