A180882 Number of permutations p() of 1..n+5 with centered difference p(i+1)-p(i-1) < 0 exactly 4 times

20, 525, 10010, 130914, 1438920, 13547688, 116189304, 917857512, 6866412696, 48911180175, 336896355510, 2249124467590, 14697484687600, 94059343340820, 593714385206800, 3693679623479664, 22778493196278456, 139016435228687562

Offset

1,1

Comments

Column 5 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, 5), "\n";
}
quit

Crossrefs

Sequence in context: A250016 A371017 A337352 * A202920 A210486 A047682

Adjacent sequences: A180879 A180880 A180881 * A180883 A180884 A180885

Keyword

nonn

Author

R. H. Hardin Sep 23 2010

Status

approved