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A154843 Triangular array, T(n,k) = s(n,k) + s(n,n-k), where s(n,k) are the Stirling numbers of the first kind. 2
2, 1, 1, 1, -2, 1, 1, -1, -1, 1, 1, -12, 22, -12, 1, 1, 14, -15, -15, 14, 1, 1, -135, 359, -450, 359, -135, 1, 1, 699, -1589, 889, 889, -1589, 699, 1, 1, -5068, 13390, -15092, 13538, -15092, 13390, -5068, 1, 1, 40284, -109038, 113588, -44835, -44835, 113588, -109038, 40284, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Except for the first two rows the row sums are zero.

LINKS

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

FORMULA

T(n,k) = s(n, k) + s(n, n - k), where s(n,k) are the Stirling numbers of the first kind (A048994).

EXAMPLE

Triangle begins as:

  2;

  1,     1;

  1,    -2,     1;

  1,    -1,    -1,      1;

  1,   -12,    22,    -12,     1;

  1,    14,   -15,    -15,    14,      1;

  1,  -135,   359,   -450,   359,   -135,     1;

  1,   699, -1589,    889,   889,  -1589,   699,     1;

  1, -5068, 13390, -15092, 13538, -15092, 13390, -5068, 1;

MATHEMATICA

Table[StirlingS1[n, k] +StirlingS1[n, n-k], {n, 0, 10}, {k, 0, n} ]//Flatten (* modified by G. C. Greubel, Apr 07 2019 *)

PROG

(PARI) {T(n, k) = stirling(n, k, 1) + stirling(n, n-k, 1)}; \\ G. C. Greubel, Apr 07 2019

(MAGMA) [[StirlingFirst(n, k) + StirlingFirst(n, n-k): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Apr 07 2019

(Sage) [[(-1)^(n-k)*(stirling_number1(n, k) + (-1)^n*stirling_number1(n, n-k)) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Apr 07 2019

CROSSREFS

Cf. A048994.

Sequence in context: A111616 A299152 A113120 * A062557 A276438 A210960

Adjacent sequences:  A154840 A154841 A154842 * A154844 A154845 A154846

KEYWORD

tabl,sign

AUTHOR

Roger L. Bagula, Jan 16 2009

STATUS

approved

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Last modified November 17 05:27 EST 2019. Contains 329217 sequences. (Running on oeis4.)