Search: id:A073165
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%I A073165
%S A073165 1,1,1,1,2,1,1,3,4,1,1,4,10,8,1,1,5,20,35,16,1,1,6,35,112,126,32,1,1,7,
%T A073165 56,294,672,462,64,1,1,8,84,672,2772,4224,1716,128,1,1,9,120,1386,9504,
%U A073165 28314,27456,6435,256,1,1,10,165,2640,28314,151008,306735,183040
%N A073165 Triangle T(n,k) read by rows: related to David G. Cantor's sigma function.
%C A073165 Square array T(n+k,k) read by antidiagonals: number of stars of length 
               k with n branches.
%C A073165 Row n of T(n+k,k) has g.f. _(floor(n/2)+1)F_(floor(n/2))(1,3/2,5/2,...,
               (2*floor(n/2)+1)/2;n,n-1,...,n-floor(n/2)+1;2^n*x) (conjecture). 
               [From Paul Barry (pbarry(AT)wit.ie), Jan 23 2009]
%D A073165 David G. Cantor, On the analogue of the division polynomials for hyperelliptic 
               curves, J. Reine Angew. Math. 447 (1994), 91-145.
%H A073165 C. Krattenthaler, A. J. Guttmann and X. G. Viennot, <a href="http://arXiv.org/
               abs/cond-mat/0006367">Vicious walkers, friendly walkers and Young 
               tableaux, II: with a wall</a>
%F A073165 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.
%F A073165 T(n+k, k) = Prod[1<=i<=j<=k, (n+i+j-1)/(i+j-1) ]. - Ralf Stephan
%e A073165 Triangle rows: 1; 1,1; 1,2,1; 1,3,4,1; 1,4,10,8,1; 1,5,20,35,16,1; ...
%o A073165 (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))/ 
               prod(i=0,(k-1)\2,binomial(2*k-2*i-1,2*i)))
%o A073165 (PARI) {T(n,k)=if(k<0|n<0, 0, prod(j=1, k, prod(i=1, j, (n-k+i+j-1)/(i+j-1) 
               )))} /* Michael Somos Oct 16 2006 */
%Y A073165 Square array has main diagonal A049505, columns include A001700, A003645, 
               A000356.
%Y A073165 Sequence in context: A098447 A162717 A122175 this_sequence A137153 A063841 
               A137596
%Y A073165 Adjacent sequences: A073162 A073163 A073164 this_sequence A073166 A073167 
               A073168
%K A073165 nonn,tabl,easy
%O A073165 0,5
%A A073165 Michael Somos, Jul 24, 2002
%E A073165 Edited by Ralf Stephan, Mar 02 2005

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