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

Comments

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

Links

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

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

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