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A155999 Triangle read by rows: t(n,m)=(-1)^(n - 2*m)*StirlingS2[n, m]*StirlingS2[n, n - m]. 0
1, 0, 0, 0, 1, 0, 0, -3, -3, 0, 0, 6, 49, 6, 0, 0, -10, -375, -375, -10, 0, 0, 15, 2015, 8100, 2015, 15, 0, 0, -21, -8820, -105350, -105350, -8820, -21, 0, 0, 28, 33782, 1014300, 2893401, 1014300, 33782, 28, 0, 0, -36, -117810, -8004150, -54009270, -54009270 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are:

{1, 0, 1, -6, 61, -770, 12160, -228382, 4989621, -124262532, 3475892685,...}

LINKS

Table of n, a(n) for n=0..50.

FORMULA

t(n,m)=(-1)^(n - 2*m)*StirlingS2[n, m]*StirlingS2[n, n - m].

EXAMPLE

{1},

{0, 0},

{0, 1, 0},

{0, -3, -3, 0},

{0, 6, 49, 6, 0},

{0, -10, -375, -375, -10, 0},

{0, 15, 2015, 8100, 2015, 15, 0},

{0, -21, -8820, -105350, -105350, -8820, -21, 0},

{0, 28, 33782, 1014300, 2893401, 1014300, 33782, 28, 0},

{0, -36, -117810, -8004150, -54009270, -54009270, -8004150, -117810, -36, 0},

{0, 45, 383250, 54860400, 778514835, 1808375625, 778514835, 54860400, 383250, 45, 0}

MATHEMATICA

Clear[t, n, m];

t[n_, m_] = (-1)^(n - 2*m)*StirlingS2[n, m]*StirlingS2[n, n - m];

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

Flatten[%]

CROSSREFS

Sequence in context: A299554 A300175 A129533 * A299904 A221768 A283071

Adjacent sequences:  A155996 A155997 A155998 * A156000 A156001 A156002

KEYWORD

tabl,uned,sign

AUTHOR

Roger L. Bagula, Feb 01 2009

STATUS

approved

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Last modified January 20 11:01 EST 2020. Contains 331083 sequences. (Running on oeis4.)