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A260196
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1, -3, followed by -1's.
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2
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1, -3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1
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OFFSET
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0,2
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COMMENTS
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1/(n+1) is the inverse Akiyama-Tanigawa transform of A164555(n)/A027642(n).
For more on the Akiyama-Tanigawa transform, see Links (correction: page 7 read here A164555 instead of A027641) and A177427.
Here:
1, -3, -1, -1, -1, -1, ...
4, -4, 0, 0, 0, 0, ...
8, -8, 0, 0, 0, 0, ...
16, -16, 0, 0, 0, 0, ...
etc.
1, 1/1, 1,
1, 4, ( 1, -1)/1, -3,
1, 4, 8, ( 2, -3, 1)/2, -1,
1, 4, 8, 16, * ( 6, -11, 6, -1)/6, = -1,
1, 4, 8, 16, 32, ( 24, -50, 35, -10, 1)/24, -1,
1, 4, 8, 16, 32, 64, (120, -274, 225, -85, 15, -1)/120, -1,
etc. etc. etc.
Via the modified Stirling numbers of the first kind, the second triangle, Iw(n), is the inverse of Worpitzky transform A163626(n).
a(n) is the third sequence of a family beginning with
1, 1, 1, 1, 1, 1, 1, 1, ... = A000012(n)
1, 0, 0, 0, 0, 0, 0, 0, 0, ... = A000007(n)
1, -3, -1, -1, -1, -1, -1, -1, -1, -1, ... .
A000012(n) is the inverse Akiyama-Tanigawa transform of A000007(n), with or without its second term.
A000007(n) is the inverse Akiyama-Tanigawa transform of A000012(n), with or without its second term.
a(n) is the inverse Akiyama-Tanigawa transform of 2^n omitting the second term i.e. 2.
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LINKS
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FORMULA
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Inverse Akiyama-Tanigawa transform of A151821(n).
a(n) = -1 for n>1.
a(n) = a(n-1) for n>2.
G.f.: -(2*x^2-4*x+1) / (x-1).
(End)
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PROG
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(PARI) first(m)=vector(m, i, i--; if(i>1, -1, if(i==0, 1, if(i==1, -3)))) \\ Anders Hellström, Aug 28 2015
(PARI) Vec(-(2*x^2-4*x+1)/(x-1) + O(x^100)) \\ Colin Barker, Sep 11 2015
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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