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A055068 Triangular array for David G. Cantor's sigma function. 1
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; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

David G. Cantor, On the analogue of the division polynomials for hyperelliptic curves, J. Reine Angew. Math. 447 (1994), 91-145.

LINKS

Table of n, a(n) for n=0..52.

FORMULA

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.

EXAMPLE

rows: 1; 1,1; 1,2,1; 1,3,4,3; 1,4,10,24,10; 1,5,20,105,160,105; ...

PROG

(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)))}

CROSSREFS

Sequence in context: A128314 A025564 A052265 * A237498 A319516 A015138

Adjacent sequences:  A055065 A055066 A055067 * A055069 A055070 A055071

KEYWORD

nonn,tabl,easy

AUTHOR

Michael Somos, Jun 12 2000

STATUS

approved

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Last modified January 20 02:57 EST 2019. Contains 319323 sequences. (Running on oeis4.)