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 A180879 Number of permutations p() of 1..n+2 with centered difference p(i+1)-p(i-1) < 0 exactly once 1
 3, 12, 50, 160, 525, 1540, 4662, 13104, 38346, 105336, 303732, 823680, 2361645, 6357780, 18208190, 48814480, 139952670, 374315656, 1075431084, 2872519104, 8273365282, 22082137896, 63760878300, 170112213600, 492371090100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Column 2 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, 2), "\n"; } quit CROSSREFS Sequence in context: A002179 A224659 A034541 * A180283 A037765 A037653 Adjacent sequences:  A180876 A180877 A180878 * A180880 A180881 A180882 KEYWORD nonn AUTHOR R. H. Hardin Sep 23 2010 STATUS approved

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Last modified January 24 22:45 EST 2022. Contains 350565 sequences. (Running on oeis4.)