%I A073253
%S A073253 1,1,1,0,1,0,0,1,1,0,0,1,2,1,0,0,0,2,2,0,0,0,0,1,3,1,0,0,0,0,0,3,3,0,0,
%T A073253 0,0,0,0,2,5,2,0,0,0,0,0,0,1,5,5,1,0,0,0,0,0,0,0,3,7,3,0,0,0,0,0,0,0,0,
%U A073253 1,7,7,1,0,0,0,0,0,0,0,0,0,5,11,5,0,0,0,0,0,0,0,0,0,0,2,11,11,2,0
%N A073253 Table of expansion of Product (1+(xy)^n/y)(1+(xy)^n/x), n>0 by antidiagonals.
%C A073253 Combinatorial interpretation is number of partitions of Gaussian integer 
               n+ki into distinct parts of form a+(a-1)i and (b-1)+bi, a,b>0.
%C A073253 Jacobi triple product identity implies the g.f. equals the Ramanujan 
               theta function divided by Product (1-(xy)^m), m>0.
%D A073253 J. H. van Lint and R. M. Wilson, A Course in Combinatorics, Cambridge 
               Univ. Press, 1992. p. 141.
%H A073253 <a href="Sindx_Ga.html#gaussians">Index entries for Gaussian integers 
               and primes</a>
%e A073253 1; 1,1; 0,1,0; 0,1,1,0; 0,1,2,1,0; 0,0,2,2,0,0; 0,0,1,3,1,0,0; ...
%o A073253 (PARI) T(n,k)=if(n<0|k<0,0,polcoeff(polcoeff(prod(i=1,max(n,k),(1+x^i*y^(i-1))*(1+x^(i-1)*y^i),
               1+x*O(x^n)+y*O(y^k)),n),k))
%Y A073253 A073252 gives antidiagonal sums.
%Y A073253 Sequence in context: A051127 A070176 A092606 this_sequence A004198 A116402 
               A093323
%Y A073253 Adjacent sequences: A073250 A073251 A073252 this_sequence A073254 A073255 
               A073256
%K A073253 nonn,tabl,easy
%O A073253 0,13
%A A073253 Michael Somos, Jul 23, 2002