A015133 - OEIS

A015133

Triangle of (Gaussian) q-binomial coefficients for q=-15.

1, 1, 1, 1, -14, 1, 1, 211, 211, 1, 1, -3164, 47686, -3164, 1, 1, 47461, 10726186, 10726186, 47461, 1, 1, -711914, 2413439311, -36190151564, 2413439311, -711914, 1, 1, 10678711, 543023133061, 122144174967811, 122144174967811, 543023133061

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OFFSET

0,5

LINKS

Table of n, a(n) for n=0..33.

Index entries related to Gaussian binomial coefficients.

FORMULA

As a triangle, T(n, k) = Product_{i=1..k} ((-15)^(n-i+1)-1)/((-15)^i-1), with 0 <= k <= n = 0,1,2,... - M. F. Hasler, Nov 05 2012

PROG

(PARI) A015133(n, r, q=-13)=prod(i=1, r, (q^(1+n-i+r)-1)/(q^i-1)) \\ (Indexing is that of the square array: n, r=0, 1, 2, ...) - M. F. Hasler, Nov 03 2012

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), A015124 (q=-11), A015125 (q=-12), A015129 (q=-13), A015132 (q=-14). - 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

Sequence in context: A174720 A060628 A022177 * A040202 A209601 A040201

Adjacent sequences: A015130 A015131 A015132 * A015134 A015135 A015136

KEYWORD

sign,tabl,easy

AUTHOR

Olivier Gérard

STATUS

approved