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A180885 Number of permutations p() of 1..n+8 with centered difference p(i+1)-p(i-1) < 0 exactly 7 times 1
126, 13104, 854700, 32369568, 917857512, 20732684544, 398942612640, 6755309074800, 103630900508850, 1466138477518000, 19428971605292964, 243734235504155968, 2921585836679480880, 33688255600558540800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 8 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, 8), "\n";

}

quit

CROSSREFS

Sequence in context: A156931 A075919 A278306 * A241172 A255172 A121004

Adjacent sequences:  A180882 A180883 A180884 * A180886 A180887 A180888

KEYWORD

nonn

AUTHOR

R. H. Hardin Sep 23 2010

STATUS

approved

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Last modified November 14 11:04 EST 2018. Contains 317182 sequences. (Running on oeis4.)