A015117 Triangle of q-binomial coefficients for q=-7.

1, 1, 1, 1, -6, 1, 1, 43, 43, 1, 1, -300, 2150, -300, 1, 1, 2101, 105050, 105050, 2101, 1, 1, -14706, 5149551, -35927100, 5149551, -14706, 1, 1, 102943, 252313293, 12328144851, 12328144851, 252313293, 102943, 1, 1, -720600, 12363454300

Offset

0,5

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), A014989 (k=1), A015258 (k=2), A015275, A015293, A015312, A015330, A015346, A015363, A015379, A015393 (k=10), A015411, A015430,... - M. F. Hasler, Nov 04 2012

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries related to Gaussian binomial coefficients.

Mathematica

Flatten[Table[QBinomial[n, m, -7], {n, 0, 10}, {m, 0, n}]] (* Harvey P. Dale, Aug 08 2012 *)

Prog

(PARI) T015117(n, k, q=-7)=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

Crossrefs

Cf. analog triangles for negative q=-2,...,-15: A015109 (q=-2), A015110 (q=-3), A015112 (q=-4), A015113 (q=-5), A015116 (q=-6), A015118 (q=-8), A015121 (q=-9), A015123 (q=-10), A015124 (q=-11), A015125 (q=-12), A015129 (q=-13), A015132 (q=-14), A015133 (q=-15);

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 04 2012

Sequence in context: A058875 A156764 A156765 * A287020 A172375 A075377

Adjacent sequences: A015114 A015115 A015116 * A015118 A015119 A015120

Keyword

sign,tabl,easy

Author

Olivier Gérard

Status

approved