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 A088857 Let Product[1+Sum[b(i,j) x^(i*j),{i,1,Infinity}],{j,1,Infinity}]=1+Sum[c(n) x^n,{n,1,Infinity}], where b(i,j) is plus or minus one and c(n) is plus or minus one or zero. Furthermore, let b(1,1)=1 (for definiteness). Then, for a given n, a(n) is the number of ways in which the coefficients b(i,j) i<=n, j<=n can be chosen. 0
 1, 2, 6, 30, 80, 634, 1424, 5392, 10677, 38052, 39051, 815616, 1421550 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In all of these series, the coefficients b(n) will be congruent, modulo 2, to the number of unrestricted partitions of n. Not much is known about the parity of the partition function, although much is known if the modulus 2 is replaced by other numbers such as 5 or 7. As for the sequence proposed here, it is not even known if it is finite or infinite. I have found coefficients satisfying the given conditions for n as large as 70. REFERENCES G. E. Andrews, The Theory of Partitions. LINKS EXAMPLE a(2)=2 because (1+x+x^2)(1-x^2)=1+x+0x^2+... and (1+x-x^2)(1+x^2)=1+x+0x^2+... But, (1+x+x^2)(1+x^2)=1+x+2x^2+... and (1+x-x^2)(1-x^2)=1+x-2x^2+... CROSSREFS Sequence in context: A117849 A328417 A290760 * A099081 A051844 A335396 Adjacent sequences:  A088854 A088855 A088856 * A088858 A088859 A088860 KEYWORD hard,nonn AUTHOR David S. Newman, Nov 29 2003 STATUS approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)