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A162169 Signed version of Pascal's triangle. 2
1, -1, 1, -1, 0, 1, 1, 0, -3, 1, 1, 0, -6, 0, 1, -1, 0, 10, 0, -5, 1, -1, 0, 15, 0, -15, 0, 1, 1, 0, -21, 0, 35, 0, -7, 1, 1, 0, -28, 0, 70, 0, -28, 0, 1, -1, 0, 36, 0, -126, 0, 84, 0, -9, 1, -1, 0, 45, 0, -210, 0, 210, 0, -45, 0, 1, 1, 0, -55, 0, 330, 0, -462, 0, 165, 0, -11, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

Related to A000111 via its matrix inverse A162170.

For odd columns k, T(n,k) = binomial(n-1, k-1) * (-1)^floor((n+k-1)/2). For even columns, T(n, k) = 1 if n = k, otherwise 0. - Mike Tryczak, Jun 17 2015

LINKS

Table of n, a(n) for n=1..78.

EXAMPLE

Table begins:

   1;

  -1,   1;

  -1,   0,   1;

   1,   0,  -3,   1;

   1,   0,  -6,   0,   1;

  -1,   0,  10,   0,  -5,   1;

  -1,   0,  15,   0, -15,   0,   1;

MATHEMATICA

nn=12; Flatten[Table[Table[If[Or[Mod[n - k, 4] == 1, Mod[n - k, 4] == 2], -1, 1]*If[n >= k, Binomial[n - 1, k - 1], 0]*If[And[n > k, Mod[k, 2] == 0], 0, 1], {k, 1, n}], {n, 1, nn}]] (* Mats Granvik, Nov 25 2017 *)

PROG

(Excel) =if(or(mod(row()-column(); 4)=1; mod(row()-column(); 4)=2); -1; 1)*if(row()>=column(); combin(row()-1; column()-1); 0)*if(and(row()>column(); mod(column(); 2)=0); 0; 1)

(PARI) T(n, k) = if (k % 2, binomial(n-1, k-1) * (-1)^floor((n+k-1)/2), if (n==k, 1 , 0));

tabl(nn) = {for (n=1, nn, for (k=1, n, print1(T(n, k), ", "); ); print(); ); } \\ Michel Marcus, Jun 17 2015

CROSSREFS

Cf. A007318, A162170.

Sequence in context: A130160 A288108 A287822 * A216954 A124801 A124926

Adjacent sequences:  A162166 A162167 A162168 * A162170 A162171 A162172

KEYWORD

sign,tabl

AUTHOR

Mats Granvik, Jun 27 2009

STATUS

approved

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Last modified February 21 14:15 EST 2018. Contains 299414 sequences. (Running on oeis4.)