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A157253
Arises in combinatorial approach to the power of 2 in the number of involutions.
1
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
OFFSET
0,4
COMMENTS
Table 1 of Kim and Kim.
LINKS
Dongsu Kim and Jang Soo Kim, A combinatorial approach to the power of 2 in the number of involutions, arXiv:0902.4311 [math.CO], 2009-2010.
FORMULA
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
PROG
(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
CROSSREFS
Sequence in context: A275441 A197465 A074933 * A003178 A079494 A169970
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Feb 25 2009
EXTENSIONS
a(7)-a(21) from Kim paper by Michel Marcus, Sep 04 2014
Missing a(19) inserted and more terms from Andrew Howroyd, May 06 2023
STATUS
approved