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A136097
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a(n) = A135951(n) /[(2^(n+1)-1) * 2^(n*(n-1)/2)].
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0
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1, -1, 5, -93, 6477, -1733677, 1816333805, -7526310334829, 124031223014725741, -8152285307423733458541, 2140200604371078953284092525, -2245805993494514875022552272042605, 9423041917569791458584837551185555483245
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| A135951 is the central terms of A135950; A135950 is the matrix inverse of A022166; A022166 is the triangle of Gaussian binomial coefficients [n,k] for q = 2.
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FORMULA
| Conjecture: the n-th central term of the matrix inverse of the triangle of Gaussian binomial coefficients in q is divisible by [(q^(n+1)-1)/(q-1) * q^(n*(n-1)/2)] for n>=0 and integer q > 1.
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PROG
| (PARI) {a(n)=local(q=2, A=matrix(2*n+1, 2*n+1, n, k, if(n>=k, if(n==1|k==1, 1, prod(j=n-k+1, n-1, 1-q^j)/prod(j=1, k-1, 1-q^j))))^-1); A[2*n+1, n+1]/( (q^(n+1)-1)/(q-1) * q^(n*(n-1)/2) )}
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CROSSREFS
| Cf. A135951, A135950, A022166.
Sequence in context: A000365 A012784 A015030 * A047052 A049662 A178018
Adjacent sequences: A136094 A136095 A136096 * A136098 A136099 A136100
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KEYWORD
| sign
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Dec 13 2007
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