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A293308
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Number of permutations of zero-one words with A056576(n)-n zeros and n-1 ones.
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1
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1, 2, 3, 10, 15, 56, 210, 330, 1287, 2002, 8008, 31824, 50388, 203490, 319770, 1307504, 2042975, 8436285, 34597290, 54627300, 225792840, 354817320, 1476337800, 6107086800, 9669554100, 40225345056, 63432274896, 265182149218, 416714805914, 1749695026860
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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a(4) = 5! / ( 2! * 3! ) = 5*4/2 = 10.
The next table shows the output using the PARI function NextPermutation(a), (cf. PROG)
[0, 0, 1, 1, 1] 1
[0, 1, 0, 1, 1] 2
[0, 1, 1, 0, 1] 3
[0, 1, 1, 1, 0] 4
[1, 0, 0, 1, 1] 5
[1, 0, 1, 0, 1] 6
[1, 0, 1, 1, 0] 7
[1, 1, 0, 0, 1] 8
[1, 1, 0, 1, 0] 9
[1, 1, 1, 0, 0] 10
(End)
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MATHEMATICA
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Table[(# - 1)!/((# - n)!*(n - 1)!) &@ Floor[n Log[2, 3]], {n, 30}] (* Michael De Vlieger, Oct 06 2017 *)
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PROG
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(PARI) /* method used in the linked paper arXiv:1709.03385 */
NextPermutation(a) = {i=#a-1; while(!(i<1 || a[i]<a[i+1]), i--); if(i<1, return(0)); k=#a; while(!(a[k]>a[i]), k--); t=a[k]; a[k]=a[i]; a[i]=t; for(k=i+1, (#a+i)/2, t=a[k]; a[k]=a[#a+1+i-k]; a[#a+1+i-k]=t); return(a)}
/* example for n = 4 */
{j=1; a=[0, 0, 1, 1, 1]; until(a==0, print(a" "j); j++; a=NextPermutation(a))} \\ Mike Winkler, Oct 30 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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