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A209036 Number of permutations of the multiset {1,1,2,2,....,n,n} with exactly  two consecutive equal terms. 0
1, 2, 36, 984, 43800, 2868480, 259554960, 31012490880, 4728875800320, 896042510496000, 206523228759724800, 56893926736333209600, 18461230471787348044800, 6968851610446509386803200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..14.

FORMULA

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.

EXAMPLE

a(1,2) = 2, because 1221 and 2112 are the only permutations of {1,1,2,2} where exactly two consecutive terms are equal.

PROG

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");

   }

CROSSREFS

Cf. A114938 (a(0,n)).

Sequence in context: A279575 A009539 A009554 * A305596 A210899 A302903

Adjacent sequences:  A209033 A209034 A209035 * A209037 A209038 A209039

KEYWORD

nonn

AUTHOR

Philippe Gibone, Mar 04 2012

STATUS

approved

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Last modified September 20 01:54 EDT 2020. Contains 337260 sequences. (Running on oeis4.)