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A127967
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A right-skewed Pascal triangle, with interspersed 1's on main diagonal.
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3
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1, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 0, 4, 0, 3, 1, 1, 0, 5, 0, 6, 0, 1, 1, 0, 6, 0, 10, 0, 4, 1, 1, 0, 7, 0, 15, 0, 10, 0, 1, 1, 0, 8, 0, 21, 0, 20, 0, 5, 1, 1, 0, 9, 0, 28
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OFFSET
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0,9
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COMMENTS
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Linked to Fibonacci numbers by row sums A127968. Inverse A127969 is linked to Genocchi numbers by its first column.
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LINKS
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FORMULA
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Column k is generated by x^(-2)*(x*(1-x)^(-1/2))^(k+2), where non-integer values are set to 0; or, column k has g.f. if(mod(k,2)=0,x^k/(1-x)^(1+k/2),x^k)
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EXAMPLE
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Triangle begins
1,
1, 1,
1, 0, 1,
1, 0, 2, 1,
1, 0, 3, 0, 1,
1, 0, 4, 0, 3, 1,
1, 0, 5, 0, 6, 0, 1,
1, 0, 6, 0, 10, 0, 4, 1,
1, 0, 7, 0, 15, 0, 10, 0, 1,
1, 0, 8, 0, 21, 0, 20, 0, 5, 1,
1, 0, 9, 0, 28, 0, 35, 0, 15, 0, 1,
1, 0, 10, 0, 36, 0, 56, 0, 35, 0, 6, 1,
1, 0, 11, 0, 45, 0, 84, 0, 70, 0, 21, 0, 1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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