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A110947
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a(n) = permanent of an n X n matrix M of zeros and ones defined as follows: if we concatenate the rows of M to form a vector v of length n^2, v_i = 1 only if i = 1 or a multiple of 2.
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1
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1, 1, 1, 0, 4, 0, 36, 0, 576, 0, 14400, 0, 518400, 0, 25401600, 0, 1625702400, 0, 131681894400, 0, 13168189440000, 0, 1593350922240000, 0, 229442532802560000, 0, 38775788043632640000, 0, 7600054456551997440000, 0
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OFFSET
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1,5
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LINKS
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FORMULA
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a(1)=a(2)=1 and for n>2: a(n)=0 if n=2*k, a(n)=k!^2 if n=2*k+1. - Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007
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PROG
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(PARI) permRWNb(a)=n=matsize(a)[1]; if(n==1, return(a[1, 1])); sg=1; in=vectorv(n); x=in; x=a[, n]-sum(j=1, n, a[, j])/2; p=prod(i=1, n, x[i]); for(k=1, 2^(n-1)-1, sg=-sg; j=valuation(k, 2)+1; z=1-2*in[j]; in[j]+=z; x+=z*a[, j]; p+=prod(i=1, n, x[i], sg)); return(2*(2*(n%2)-1)*p) A110947(n)=if(n==2, 1, if(n%2, ((n-1)/2)!^2)) for(n=1, 42, a=matrix(n, n, i, j, 1-((i-1)*n+j)%2); a[1, 1]=1; print1(permRWNb(a)", ")) for(n=1, 42, print1(A110947(n)", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007
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CROSSREFS
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Odd-indexed terms are the same as A001044.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007
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STATUS
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approved
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