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Search: id:A134433
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| A134433 |
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Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} in which the last entry of the first increasing run is equal to k (1<=k<=n). |
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+0
1
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| 1, 0, 2, 0, 1, 5, 0, 2, 6, 16, 0, 6, 16, 33, 65, 0, 24, 60, 114, 196, 326, 0, 120, 288, 522, 848, 1305, 1957, 0, 720, 1680, 2952, 4632, 6850, 9786, 13700, 0, 5040, 11520, 19800, 30336, 43710, 60672, 82201, 109601
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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T(n,n)=A000522(n-1) (number of arrangements of {1,2,...,n-1}). T(n,2)=(n-2)! for n>=3. Sum(k*T(n,k),k=1..n)=A056542(n+1).
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FORMULA
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T(n,k)=Sum[(n-j-1)!(k-j)binom(k-1,j-1), j=1..k-1) for k<n; T(n,n)=(n-1)!Sum(1/j!, j=0..n-1).
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EXAMPLE
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T(4,3)=6 because we have 3124, 3142, 3214, 3241, 1324, and 2314.
Triangle starts:
1;
0,2;
0,1,5;
0,2,6,16;
0,6,16,33,65;
0.24.60.114.196.326;
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MAPLE
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T:=proc(n, k): if k < n then sum(factorial(k-1)*factorial(n-j-1)/(factorial(j-1)*factorial(k-j-1)), j=1..k-1) elif k = n then factorial(n-1)*(sum(1/factorial(j), j = 0 .. n-1)) else 0 end if end proc: for n to 9 do seq(T(n, k), k=1..n) end do; # yields sequence in triangular form
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CROSSREFS
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Cf. A000522, A056542.
Sequence in context: A016584 A112899 A108263 this_sequence A125183 A092583 A079134
Adjacent sequences: A134430 A134431 A134432 this_sequence A134434 A134435 A134436
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 22 2007
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