A180879 Number of permutations p() of 1..n+2 with centered difference p(i+1)-p(i-1) < 0 exactly once

3, 12, 50, 160, 525, 1540, 4662, 13104, 38346, 105336, 303732, 823680, 2361645, 6357780, 18208190, 48814480, 139952670, 374315656, 1075431084, 2872519104, 8273365282, 22082137896, 63760878300, 170112213600, 492371090100

Offset

1,1

Comments

Column 2 of A180887

Links

R. H. Hardin, Table of n, a(n) for n=1..100

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(n=1; n<=100; n++) {
print n, " ", t(n, 2), "\n";
}
quit

Crossrefs

Sequence in context: A002179 A224659 A034541 * A180283 A037765 A037653

Adjacent sequences: A180876 A180877 A180878 * A180880 A180881 A180882

Keyword

nonn

Author

R. H. Hardin Sep 23 2010

Status

approved