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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 9
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A173094 A087989 A103356

Adjacent sequences:  A180884 A180885 A180886 * A180888 A180889 A180890

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Sep 23 2010

STATUS

approved

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Last modified October 14 00:30 EDT 2019. Contains 327991 sequences. (Running on oeis4.)