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A180884 Number of permutations p() of 1..n+7 with centered difference p(i+1)-p(i-1) < 0 exactly 6 times 1
70, 4662, 203616, 5517204, 116189304, 1997701992, 29868078240, 398942612640, 4892905415970, 55931879316170, 604691896711760, 6237809698157180, 61935775158718032, 595207094582803248, 5567411131221296448 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 7 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, 7), "\n";

}

quit

CROSSREFS

Sequence in context: A319735 A258374 A146349 * A238540 A060057 A049216

Adjacent sequences:  A180881 A180882 A180883 * A180885 A180886 A180887

KEYWORD

nonn

AUTHOR

R. H. Hardin Sep 23 2010

STATUS

approved

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Last modified June 15 13:25 EDT 2021. Contains 345048 sequences. (Running on oeis4.)