

A177264


Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having k as the first entry in the last block (1<=k<=n). A block of a permutation is a maximal sequence of consecutive integers which appear in consecutive positions. For example, the permutation 45123867 has 4 blocks: 45, 123, 8, and 67.


1



1, 2, 0, 4, 1, 1, 10, 5, 5, 4, 34, 23, 23, 22, 18, 154, 119, 119, 118, 114, 96, 874, 719, 719, 718, 714, 696, 600, 5914, 5039, 5039, 5038, 5034, 5016, 4920, 4320, 46234, 40319, 40319, 40318, 40314, 40296, 40200, 39600, 35280, 409114, 362879, 362879, 362878
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OFFSET

1,2


COMMENTS

Sum of entries in row n is n!.
Mirror image of A177263.
T(n,1)=A003422(n).


REFERENCES

A. N. Myers, Counting permutations by their rigid patterns, J. Combin. Theory, A 99 (2002), 345357.


LINKS

Table of n, a(n) for n=1..49.


FORMULA

T(n,k)=(n1)!(k2)! if 2<=k<=n; T(n,1)=0!+1!+...+(n1)!.


EXAMPLE

T(4,3)=5 because we have 1243, 2134, 2143, 2413, and 4213 (the blocks are separated by dashes).
Triangle starts:
1;
2,0;
4,1,1;
10,5,5,4;
34,23,23,22,18;


MAPLE

T := proc (n, k) if 2 <= k and k <= n then factorial(n1)factorial(k2) elif k = 1 then sum(factorial(j), j = 0 .. n1) else 0 end if end proc: for n to 10 do seq(T(n, k), k = 1 .. n) end do; # yields sequence in triangular form


CROSSREFS

Cf. A003422, A177263.
Sequence in context: A264379 A090888 A154794 * A326758 A318366 A300252
Adjacent sequences: A177261 A177262 A177263 * A177265 A177266 A177267


KEYWORD

nonn,tabl


AUTHOR

Emeric Deutsch, May 16 2010


STATUS

approved



