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A055068
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Triangular array for David G. Cantor's sigma function.
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1
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1, 1, 1, 1, 2, 1, 1, 3, 4, 3, 1, 4, 10, 24, 10, 1, 5, 20, 105, 160, 105, 1, 6, 35, 336, 1260, 3360, 1260, 1, 7, 56, 882, 6720, 48510, 80640, 48510, 1, 8, 84, 2016, 27720, 443520, 2162160, 6209280, 2162160, 1, 9, 120, 4158, 95040, 2972970, 34594560, 312161850
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n, k)*T(n-2, k-1)-2*T(n-1, k-1)*T(n-1, k)+T(n, k-1)*T(n-2, k)=0.
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EXAMPLE
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Triangle rows:
1;
1,1;
1,2,1;
1,3,4,3;
1,4,10,24,10;
1,5,20,105,160,105;
...
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PROG
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(PARI) {T(n, k) = if( k<0 || k>n, 0, prod( i=1, (k+1)\2, binomial(n + 2*i - 1 - k%2, 4*i - 1 - k%2*2)))}
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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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