0,4

T(n,k) = A007318(n+1,k+1) - A007318(n+1,k), 0<=k<=n, i.e. first differences of rows in Pascal's triangle;

T(n,k) = -T(n,k);

row sums and central terms equal 0, cf. A000004;

sum of positive elements of n-th row = A014495(n+1);

T(n,0) = n;

T(n,1) = A000096(n-2) for n > 1; T(n,1) = - A080956(n) for n > 0;

T(n,2) = A005586(n-4) for n > 3; T(n,2) = A129936(n-2);

T(n,3) = A005587(n-6) for n > 5;

T(n,4) = A005557(n-9) for n > 8;

T(n,5) = A064059(n-11) for n > 10;

T(n,6) = A064061(n-13) for n > 12;

T(n,7) = A124087(n) for n > 14;

T(n,8) = A124088(n) for n > 16;

T(2*n+1,n) = T(2*n+2,n) = A000108(n+1), Catalan numbers;

T(2*n+3,n) = A000245(n+2);

T(2*n+4,n) = A002057(n+1);

T(2*n+5,n) = A000344(n+3);

T(2*n+6,n) = A003517(n+3);

T(2*n+7,n) = A000588(n+4);

T(2*n+8,n) = A003518(n+4);

T(2*n+9,n) = A001392(n+5);

T(2*n+10,n) = A003519(n+5);

T(2*n+11,n) = A000589(n+6);

T(2*n+12,n) = A090749(n+6);

T(2*n+13,n) = A000590(n+7).

Reinhard Zumkeller, Rows n=0..150 of triangle, flattened

Index entries for triangles and arrays related to Pascal's triangle

The triangle begins:

.   0:                              0

.   1:                            1   -1

.   2:                          2   0   -2

.   3:                       3    2   -2   -3

.   4:                     4    5   0   -5   -4

.   5:                  5    9    5   -5   -9   -5

.   6:                6   14   14   0  -14  -14   -6

.   7:             7   20   28   14  -14  -28  -20   -7

.   8:           8   27   48   42   0  -42  -48  -27   -8

.   9:        9   35   75   90   42  -42  -90  -75  -35   -9

.  10:     10   44  110  165  132   0 -132 -165 -110  -44  -10

.  11:  11   54  154  275  297  132 -132 -297 -275 -154  -54  -11  .

(Haskell)

a214292 n k = a214292_tabl !! n !! k

a214292_row n = a214292_tabl !! n

a214292_tabl = map diff $ tail a007318_tabl

   where diff row = zipWith (-) (tail row) row

Cf. A007318, A000004, A000096, A000108, A000245, A000344, A000588, A000589, A000590, A001392, A002057, A003517, A003518, A003519, A005557, A005586, A005587, A008313, A014495, A064059, A064061, A080956, A090749, A097808, A112467, A124087, A124088, A129936, A259525.

Sequence in context: A104513 A220455 A208295 * A212184 A033769 A074660

Adjacent sequences:  A214289 A214290 A214291 * A214293 A214294 A214295

sign,tabl

Reinhard Zumkeller, Jul 12 2012

approved