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A155825 A triangular sequence: t(n,m)=(-1)^(n - 2*m)*n!*StirlingS1[n, m]StirlingS1[n, n - m]/Binomial[n, m]. 0
1, 0, 0, 0, 1, 0, 0, 12, 12, 0, 0, 216, 484, 216, 0, 0, 5760, 21000, 21000, 5760, 0, 0, 216000, 1117920, 1822500, 1117920, 216000, 0, 0, 10886400, 74088000, 171884160, 171884160, 74088000, 10886400, 0, 0, 711244800, 6059370240, 18531878400 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are:

{1, 0, 1, 24, 916, 53520, 4490340, 513717120, 76996938816, 14652924572160,

3453133797288000,...}

LINKS

Table of n, a(n) for n=0..39.

FORMULA

t(n,m)=(-1)^(n - 2*m)*n!*StirlingS1[n, m]StirlingS1[n, n - m]/Binomial[n, m].

EXAMPLE

1},

{0, 0},

{0, 1, 0},

{0, 12, 12, 0},

{0, 216, 484, 216, 0},

{0, 5760, 21000, 21000, 5760, 0},

{0, 216000, 1117920, 1822500, 1117920, 216000, 0},

{0, 10886400, 74088000, 171884160, 171884160, 74088000, 10886400, 0},

{0, 711244800, 6059370240, 18531878400, 26391951936, 18531878400, 6059370240, 711244800, 0},

{0, 58525286400, 603115269120, 2314701204480, 4350120526080, 4350120526080, 2314701204480, 603115269120, 58525286400, 0},

{0, 5925685248000, 72021287116800, 335120133600000, 791240912179200, 1044517761000000, 791240912179200, 335120133600000, 72021287116800, 5925685248000, 0}

MATHEMATICA

t[n_, m_] = (-1)^(n - 2* m)*n!*StirlingS1[n, m]StirlingS1[n, n - m]/Binomial[n, m];

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

Flatten[%]

CROSSREFS

Sequence in context: A254717 A195748 A038337 * A125509 A281251 A247511

Adjacent sequences:  A155822 A155823 A155824 * A155826 A155827 A155828

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 28 2009

STATUS

approved

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Last modified December 4 14:49 EST 2020. Contains 338924 sequences. (Running on oeis4.)