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A155999 Triangle T(n, k) = (-1)^n*StirlingS2(n, k)*StirlingS2(n, n-k), read by rows. 1
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 (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

G. C. Greubel, Rows n = 0..100 of the triangle, flattened

FORMULA

T(n, k) = (-1)^n*StirlingS2(n, k)*StirlingS2(n, n-k)

EXAMPLE

Triangle begins as:

  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;

MATHEMATICA

T[n_, k_]:= (-1)^n*StirlingS2[n, k]*StirlingS2[n, n-k];

Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten

PROG

(Sage)

def A155999(n, k): return (-1)^n*stirling_number2(n, k)*stirling_number2(n, n-k)

flatten([[A155999(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 27 2021

(Magma)

A155999:= func< n, k | (-1)^n*StirlingSecond(n, k)*StirlingSecond(n, n-k) >;

[A155999(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 27 2021

(PARI) T(n, k) = (-1)^n*stirling(n, k, 2)*stirling(n, n-k, 2);

matrix(10, 10, n, k, n--; k--; if (n>=k, T(n, k))) \\ Michel Marcus, Feb 27 2021

CROSSREFS

Cf. A048993.

Sequence in context: A299554 A300175 A129533 * A338034 A299904 A221768

Adjacent sequences:  A155996 A155997 A155998 * A156000 A156001 A156002

KEYWORD

tabl,sign

AUTHOR

Roger L. Bagula, Feb 01 2009

EXTENSIONS

Edited by G. C. Greubel, Feb 27 2021

STATUS

approved

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Last modified August 19 03:31 EDT 2022. Contains 356216 sequences. (Running on oeis4.)