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A180880
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Number of permutations p() of 1..n+3 with centered difference p(i+1)-p(i-1) < 0 exactly twice
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1
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6, 50, 360, 1960, 10010, 45738, 203616, 854700, 3560172, 14299428, 57595824, 226022940, 895687650, 3473777450, 13672916400, 52745436172, 207268333844, 798176908620, 3139574496240, 12092845015888, 47667323303236
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OFFSET
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1,1
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COMMENTS
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Column 3 of A180887
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LINKS
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R. H. Hardin, Table of n, a(n) for n=1..100
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PROG
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/* 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
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CROSSREFS
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Sequence in context: A220887 A213807 A223816 * A027330 A090409 A212233
Adjacent sequences: A180877 A180878 A180879 * A180881 A180882 A180883
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin Sep 23 2010
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STATUS
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approved
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