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A171998 A(n,k,m) is the (n,k)-th entry of the matrix inverting the matrix consisting of (-1)^(n-k) times the number of permutations of an n-set with k disjoint cycles of length less than or equal to m as the (n,k)-th entry, called the m-restrained 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

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

REFERENCES

Multi-restrained Stirling numbers (just submitted)

LINKS

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

FORMULA

Explicit Formula A(n,k,m)= A(n-1,k-1,m)- Sum_{i=1}^{m-1} (-1)^{i}(k)...(k+i-1) A(n, k+i,m) A(n,k,m) = A(n-1,k-1,m) + k A(n-1,k,m) + (-1)^m k(k+1)...(k+m-1)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

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Last modified November 18 16:04 EST 2018. Contains 317323 sequences. (Running on oeis4.)