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A015116
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Triangle of q-binomial coefficients for q=-6.
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13
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1, 1, 1, 1, -5, 1, 1, 31, 31, 1, 1, -185, 1147, -185, 1, 1, 1111, 41107, 41107, 1111, 1, 1, -6665, 1480963, -8838005, 1480963, -6665, 1, 1, 39991, 53308003, 1910490043, 1910490043, 53308003, 39991, 1, 1, -239945, 1919128099, -412612541285
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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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), A014987 (k=1), A015257 (k=2), A015273, A015292, A015310, A015328, A015345, A015361, A015378, A015392 (k=10), A015410, A015429,... - M. F. Hasler, Nov 04 2012
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LINKS
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Table of n, a(n) for n=0..39.
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PROG
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(PARI) T015116(n, k, q=-6)=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
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CROSSREFS
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Cf. analog triangles for other q: A015109 (q=-2), A015110 (q=-3), A015112 (q=-4), A015113 (q=-5), 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
Sequence in context: A172377 A156587 A058720 * A174790 A156691 A246051
Adjacent sequences: A015113 A015114 A015115 * A015117 A015118 A015119
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KEYWORD
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sign,tabl,easy
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AUTHOR
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Olivier Gérard
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STATUS
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approved
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