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 A073253 Table of expansion of Product (1+(xy)^n/y)(1+(xy)^n/x), n>0 by antidiagonals. 0
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). 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. Jacobi triple product identity implies the g.f. equals the Ramanujan theta function divided by Product (1-(xy)^m), m>0. REFERENCES J. H. van Lint and R. M. Wilson, A Course in Combinatorics, Cambridge Univ. Press, 1992. p. 141. LINKS Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions EXAMPLE {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}; ... PROG (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))} CROSSREFS A073252 gives antidiagonal sums. Sequence in context: A070176 A092606 A275948 * A004198 A324351 A116402 Adjacent sequences:  A073250 A073251 A073252 * A073254 A073255 A073256 KEYWORD nonn,tabl,easy AUTHOR Michael Somos, Jul 23 2002 STATUS approved

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Last modified May 17 21:11 EDT 2021. Contains 343990 sequences. (Running on oeis4.)