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A156815 Triangle read by rows: t(n,m)=n!*StirlingS2[n, m]/Binomial[n, m]. 0
1, 0, 1, 0, 1, 2, 0, 2, 6, 6, 0, 6, 28, 36, 24, 0, 24, 180, 300, 240, 120, 0, 120, 1488, 3240, 3120, 1800, 720, 0, 720, 15120, 43344, 50400, 33600, 15120, 5040, 0, 5040, 182880, 695520, 979776, 756000, 383040, 141120, 40320, 0, 40320, 2570400, 13068000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Row sums are:

{1, 1, 3, 14, 94, 864, 10488, 163344, 3183696, 75977280, 2178103680,...}.

In the previously submitted sequence, A156811, I misread Steve Roman's superscript as a power:

StirlingS2[n,m]=Binomial[n,m]*Bernoulli[n-m,0]_(-m).

This sequence gives:

t(n,m)=n!*Bernoulli[n-m,0]_(-m).

REFERENCES

Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), page 99.

LINKS

Table of n, a(n) for n=0..48.

FORMULA

t(n,m)=n!*StirlingS2[n, m]/Binomial[n, m].

EXAMPLE

{1},

{0, 1},

{0, 1, 2},

{0, 2, 6, 6},

{0, 6, 28, 36, 24},

{0, 24, 180, 300, 240, 120},

{0, 120, 1488, 3240, 3120, 1800, 720},

{0, 720, 15120, 43344, 50400, 33600, 15120, 5040},

{0, 5040, 182880, 695520, 979776, 756000, 383040, 141120, 40320},

{0, 40320, 2570400, 13068000, 22377600, 20018880, 11430720, 4656960, 1451520, 362880},

{0, 362880, 41207040, 282139200, 589334400, 612360000, 394450560, 177811200, 60480000, 16329600, 3628800}

MATHEMATICA

Clear[t, n, m];

t[n_, m_] = n!*StirlingS2[n, m]/Binomial[n, m];

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A291799 A295027 A225479 * A303439 A303345 A175802

Adjacent sequences:  A156812 A156813 A156814 * A156816 A156817 A156818

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 16 2009

STATUS

approved

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Last modified May 11 09:11 EDT 2021. Contains 343788 sequences. (Running on oeis4.)