

A171998


A(n,k,m) is the (n,k)th entry of the matrix inverting the matrix consisting of (1)^(nk) times the number of permutations of an nset with k disjoint cycles of length less than or equal to m as the (n,k)th entry, called the mrestrained Stirling numbers of the second kind. The example above shows the case m=3.


1



1, 1, 1, 1, 3, 1, 5, 7, 6, 1, 65, 15, 25, 10, 1, 455, 455, 0, 65, 15, 1, 1295, 4725, 1715, 140, 140, 21, 1
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OFFSET

1,5


COMMENTS

A(n,k,m) also can be expanded for nonpositive integers n and k using the multirestrained Stirling numbers of the first kind.


REFERENCES

Multirestrained Stirling numbers (just submitted)


LINKS

Table of n, a(n) for n=1..28.


FORMULA

Explicit Formula A(n,k,m)= A(n1,k1,m) Sum_{i=1}^{m1} (1)^{i}(k)...(k+i1) A(n, k+i,m) A(n,k,m) = A(n1,k1,m) + k A(n1,k,m) + (1)^m k(k+1)...(k+m1)A(n,k+m,m)


EXAMPLE

A(1,1,3)=1,A(1,2,3)=0,A(1,3,3)=0,A(1,4,3)=0,... A(2,1,3)=1,A(2,2,3)=1,A(2,3,3)=0,A(2,4,3)=0,... A(3,1,3)=1,A(3,2,3)=3,A(3,3,3)=1,A(3,4,3)=0,... A(4,1,3)=5,A(4,2,3)=7,A(4,3,3)=6,A(4,4,3)=1,...


CROSSREFS

Cf. A111246, 144633
Sequence in context: A077020 A107920 A169998 * A159285 A021080 A049764
Adjacent sequences: A171995 A171996 A171997 * A171999 A172000 A172001


KEYWORD

sign


AUTHOR

Ji Young Choi (jychoi(AT)ship.edu), Jan 21 2010


STATUS

approved



