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A142473 A division triangle sequence of the Stirling numbers of the first kind by the binomial ( Pascal's triangle): t(n,m)=n!*StirlingS1[n, m]/Binomial[n, m]. 0
1, -1, 2, 4, -6, 6, -36, 44, -36, 24, 576, -600, 420, -240, 120, -14400, 13152, -8100, 4080, -1800, 720, 518400, -423360, 233856, -105840, 42000, -15120, 5040, -25401600, 18817920, -9455040, 3898944, -1411200, 463680, -141120, 40320, 1625702400, -1104606720, 510295680, -193777920, 64653120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums are:

{1, 1, 4, -4, 276, -6348, 254976, -13188096, 887086080, -74869297920}.

REFERENCES

t(n,m)=n!*StirlingS1[n, m]/Binomial[n, m].

LINKS

Table of n, a(n) for n=1..41.

FORMULA

t(n,m)=n!*StirlingS1[n, m]/Binomial[n, m].

EXAMPLE

{1},

{-1, 2},

{4, -6, 6},

{-36, 44, -36, 24},

{576, -600, 420, -240, 120},

{-14400, 13152, -8100, 4080, -1800, 720},

{518400, -423360, 233856, -105840, 42000, -15120, 5040},

{-25401600, 18817920, -9455040, 3898944, -1411200, 463680, -141120, 40320},

{1625702400, -1104606720, 510295680, -193777920, 64653120, -19595520, 5503680, -1451520, 362880},

{-131681894400, 82783088640, -35462448000, 12505190400, -3878280000, 1093357440, -285768000, 70156800, -16329600, 3628800}

MATHEMATICA

t[n_, m_] = n!*StirlingS1[n, m]/Binomial[n, m]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]

CROSSREFS

Sequence in context: A286894 A225187 A281485 * A132426 A072646 A091476

Adjacent sequences:  A142470 A142471 A142472 * A142474 A142475 A142476

KEYWORD

sign,uned

AUTHOR

Roger L. Bagula and Gary W. Adamson, Sep 21 2008

STATUS

approved

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Last modified August 9 00:34 EDT 2020. Contains 336309 sequences. (Running on oeis4.)