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Search: id:A073253
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| A073253 |
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Table of expansion of Product (1+(xy)^n/y)(1+(xy)^n/x), n>0 by antidiagonals. |
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+0
1
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| 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; listen)
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OFFSET
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0,13
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COMMENT
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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.
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REFERENCES
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J. H. van Lint and R. M. Wilson, A Course in Combinatorics, Cambridge Univ. Press, 1992. p. 141.
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LINKS
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Index entries for Gaussian integers and primes
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EXAMPLE
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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; ...
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PROGRAM
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(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))
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CROSSREFS
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A073252 gives antidiagonal sums.
Adjacent sequences: A073250 A073251 A073252 this_sequence A073254 A073255 A073256
Sequence in context: A051127 A070176 A092606 this_sequence A004198 A116402 A093323
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Michael Somos, Jul 23, 2002
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