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A209036
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Number of permutations of the multiset {1,1,2,2,....,n,n} with exactly two consecutive equal terms.
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0
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1, 2, 36, 984, 43800, 2868480, 259554960, 31012490880, 4728875800320, 896042510496000, 206523228759724800, 56893926736333209600, 18461230471787348044800, 6968851610446509386803200
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OFFSET
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1,2
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COMMENTS
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This is a particular case (p = 1) of the more general: a(p,n) = number of permutations of the multiset {1,1,2,2,....,n,n} with exactly p times two consecutive equal terms. The sequence a(0,p) is A114938.
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LINKS
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FORMULA
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a(1,1) = 1; a(p,n+1) = a[p, n + 1] = (2*n - p + 2)*a[p-1, n] + (2*n - p + 1)*(2*n - p)*a[p, n]/2 + p*a[p, n] + (p + 1)*(2*n - p)*a[p + 1, n + (p + 2)*(p + 1)*a[p + 2, n]/2.
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EXAMPLE
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a(1,2) = 2, because 1221 and 2112 are the only permutations of {1,1,2,2} where exactly two consecutive terms are equal.
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PROG
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C-Language :
for (p = 0; p < 20; p++)
a[p][0] = 0;
for (n = 0; n < 20; n++)
a[0][n] = 0;
a[1][0] = 1;
for (n = 0; n < 18; n++)
for (p = 0; p < 18; p++)
a[p+1][n + 1] = (2*n - p + 2)*a[p][n] + (2*n - p + 1)*(2*n - p)*a[p+1][n]/2 + p*a[p+1][n] + (p + 1)*(2*n - p)*a[p + 2][n] + (p + 2)*(p + 1)*a[p + 3][n]/2 ;
for(n = 0; n < 10; n++)
{
printf("%d, %ld ", n, a[2][n]);
if (n % 5 == 0)
printf("\n\n");
}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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