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Search: id:A055068
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| A055068 |
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Triangular array for David G. Cantor's sigma function. |
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+0
2
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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
(list; table; graph; listen)
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OFFSET
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0,5
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REFERENCES
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David G. Cantor, On the analogue of the division polynomials for hyperelliptic curves, J. Reine Angew. Math. 447 (1994), 91-145.
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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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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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PROGRAM
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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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Sequence in context: A128314 A025564 A052265 this_sequence A015138 A100529 A124424
Adjacent sequences: A055065 A055066 A055067 this_sequence A055069 A055070 A055071
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Michael Somos
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