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A157253
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Arises in combinatorial approach to the power of 2 in the number of involutions.
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1
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1, 1, 1, 2, 2, 6, 8, 26, 41, 145, 253, 978, 1858, 7726, 15796, 69878, 152219, 711243, 1638323, 8039510, 19467494, 99862594, 252998224, 1351486758, 3568259503, 19786100599, 54263159347, 311482467134, 884834059454, 5245588599330, 15397757661092
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OFFSET
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0,4
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COMMENTS
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Table 1 of Kim and Kim.
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LINKS
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FORMULA
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a(2*n) = a(2*n-2) + (n-1)*a(2*n-3) + 2*binomial(n-1, 2)*a(2*n-4) + 3*binomial(n-1, 3)*a(2*n-8); a(2*n+1) = a(2*n) + n*a(2*n-1). See eqn. 5 and 6 for g_n(1,1) in Kim and Kim reference. - Andrew Howroyd, May 07 2023
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PROG
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(PARI)
seq(n)={my(a=vector(n+1)); a[1]=a[2]=1; for(n=2, n, a[n+1] = if(n%2==0, a[n-1] + if(n>=3, (n/2-1)*a[n-2]) + if(n>=4, 2*binomial(n/2-1, 2)*a[n-3]) + if(n>=8, 3*binomial(n/2-1, 3)*a[n-7]), a[n] + (n-1)*a[n-1]/2)); a} \\ Andrew Howroyd, May 06 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Missing a(19) inserted and more terms from Andrew Howroyd, May 06 2023
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STATUS
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approved
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