A015124 Triangle of q-binomial coefficients for q=-11.

1, 1, 1, 1, -10, 1, 1, 111, 111, 1, 1, -1220, 13542, -1220, 1, 1, 13421, 1637362, 1637362, 13421, 1, 1, -147630, 198134223, -2177691460, 198134223, -147630, 1, 1, 1623931, 23974093353, 2898705467483, 2898705467483, 23974093353, 1623931, 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 in the former, or row/columns in the latter, are then (k=0,...,12): A000012, A014993, A015262, A015279, A015300, A015317, A015334, A015353, A015368, A015383, A015499, A015418, A015434. - M. F. Hasler, Nov 04 & Nov 05 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), 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

PARI

T015124(n, k, q=-11)=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