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A155744 Triangle T(n, k) = (-1)^(n-k)*StirlingS1(n, k) + (-1)^k*StirlingS1(n, n-k) + (-1)^n*StirlingS1(n, k)*StirlingS1(n, n-k), read by rows. 1
3, 1, 1, 1, 3, 1, 1, 11, 11, 1, 1, 48, 143, 48, 1, 1, 274, 1835, 1835, 274, 1, 1, 1935, 23649, 51075, 23649, 1935, 1, 1, 15861, 310639, 1195999, 1195999, 310639, 15861, 1, 1, 146188, 4221286, 25753812, 45832899, 25753812, 4221286, 146188, 1, 1, 1491876, 59942994, 535933124, 1510548249, 1510548249, 535933124, 59942994, 1491876, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

FORMULA

T(n, k) = (-1)^(n-k)*StirlingS1(n, k) + (-1)^k*StirlingS1(n, n-k) + (-1)^n*StirlingS1(n, k)*StirlingS1(n, n-k).

Sum_{k=0..n} T(n, k) = 2*n! + A342111(n). - G. C. Greubel, Jun 05 2021

EXAMPLE

  3;

  1,      1;

  1,      3,       1;

  1,     11,      11,        1;

  1,     48,     143,       48,        1;

  1,    274,    1835,     1835,      274,        1;

  1,   1935,   23649,    51075,    23649,     1935,       1;

  1,  15861,  310639,  1195999,  1195999,   310639,   15861,      1;

  1, 146188, 4221286, 25753812, 45832899, 25753812, 4221286, 146188, 1;

MATHEMATICA

T[n_, k_] = (-1)^(n-k)*StirlingS1[n, k] + (-1)^k*StirlingS1[n, n-k] + (-1)^n*StirlingS1[n, k]*StirlingS1[n, n-k];

Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jun 05 2021 *)

PROG

(MAGMA)

A155744:= func< n, k | (-1)^n*StirlingFirst(n, k)*StirlingFirst(n, n-k) + (-1)^k*StirlingFirst(n, n-k) + (-1)^(n-k)*StirlingFirst(n, k) >;

[A155744(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 05 2021

(Sage)

def A155744(n, k): return stirling_number1(n, k)*stirling_number1(n, n-k) + stirling_number1(n, k) + stirling_number1(n, n-k)

flatten([[A155744(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 05 2021

CROSSREFS

Cf. A000142, A001263, A048994, A342111.

Sequence in context: A226203 A327791 A051997 * A086869 A095345 A342671

Adjacent sequences:  A155741 A155742 A155743 * A155745 A155746 A155747

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Jan 26 2009

EXTENSIONS

Edited by G. C. Greubel, Jun 05 2021

STATUS

approved

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Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)