A180887 Array read by antidiagonals: T(n,k)=number of permutations p() of 1..n+k with centered difference p(i+1)-p(i-1) < 0 exactly k-1 times.

2, 3, 3, 6, 12, 6, 10, 50, 50, 10, 20, 160, 360, 160, 20, 35, 525, 1960, 1960, 525, 35, 70, 1540, 10010, 17080, 10010, 1540, 70, 126, 4662, 45738, 130914, 130914, 45738, 4662, 126, 252, 13104, 203616, 877968, 1438920, 877968, 203616, 13104, 252, 462, 38346

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n=1..10000

Example

Table starts:
    2      3        6        10          20            35             70
    3     12       50       160         525          1540           4662
    6     50      360      1960       10010         45738         203616
   10    160     1960     17080      130914        877968        5517204
   20    525    10010    130914     1438920      13547688      116189304
   35   1540    45738    877968    13547688     174550992     1997701992
   70   4662   203616   5517204   116189304    1997701992    29868078240
  126  13104   854700  32369568   917857512   20732684544   398942612640
  252  38346  3560172 183346020  6866412696  200430861345  4892905415970
  462 105336 14299428 997586304 48911180175 1825340594220 55931879316170

Prog

(bc)
/* Formula r(n, k) from A000892 */
define factorial(n) {
auto prod;
prod=1;
while(n>=2)prod*=n--;
return prod;
}
define binomial(n, i) {
if(i<0||i>n)return 0;
return factorial(n)/(factorial(i)*factorial(n-i));
}
define r(n, k) {
auto j, sum;
sum=0;
for(j=0; j<=k+1; j++) {
sum+=(-1)^j*(k+1-j)^n*binomial(n+1, j);
}
return sum;
}
define t(n, k) {
auto sum, i;
sum=0;
for(i=0; i<=(k-1); i++)sum+=r((n+k)/2, i)*r((n+k)-(n+k)/2, (k-1)-i);
return sum*binomial((n+k), (n+k)/2);
}
for(index=1; index<=10000; index++) {
n=n+1; k=k-1; if(k<=0) { k=n; n=1; }
print index, " ", t(n, k), "\n";
}
quit

Crossrefs

Columns 1..9 are A001405(n+1), A180879, A180880, A180881, A180882, A180883, A180884, A180885, A180886.

Sequence in context: A124063 A054630 A049875 * A329748 A173094 A087989

Adjacent sequences: A180884 A180885 A180886 * A180888 A180889 A180890

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 23 2010

Status

approved