A180880 Number of permutations p() of 1..n+3 with centered difference p(i+1)-p(i-1) < 0 exactly twice

6, 50, 360, 1960, 10010, 45738, 203616, 854700, 3560172, 14299428, 57595824, 226022940, 895687650, 3473777450, 13672916400, 52745436172, 207268333844, 798176908620, 3139574496240, 12092845015888, 47667323303236

Offset

1,1

Comments

Column 3 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, 3), "\n";
}
quit

Crossrefs

Sequence in context: A241781 A272469 A223816 * A308860 A318162 A027330

Adjacent sequences: A180877 A180878 A180879 * A180881 A180882 A180883

Keyword

nonn

Author

R. H. Hardin Sep 23 2010

Status

approved