0,5

Row sum of the unsigned triangle = A028361: (1, 2, 6, 30, 270, 4590,...). Right border of the unsignd triangle = A006125: (1, 1, 2, 8, 64, 1024,...).

Unsigned triangle : A077957(n) DELTA A007179(n+1) = [1,0,2,0,4,0,8,0,16,0,32,0,...]DELTA[1,1,4,6,16,28,64,120,256,496,...], where DELTA is the operator defined in A084938 . Signed triangle : [1,0,2,0,4,0,8,0,16,0,...]DELTA[ -1,-1,-4,-6,-16,-28,-64,...]. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 20 2009]

Triangle read by rows, n-th row = n-th degree polynomial as expansion of (x-1)*(x-2)*(x-4)*...*(x-2^(n-1))

First few rows of the unsigned triangle =

1;

1, 1;

1, 3, 2;

1, 7, 14, 8;

1, 15, 70, 120, 64;

1, 31, 310, 1240, 1984, 1024;

1, 63, 1302, 11160, 41664, 64512, 32768;

1, 127, 5334, 94488, 755904, 2731008, 4162536, 2097152;

1, 255, 21590, 777240, 12850368, 99486720, 353730560, 534773760, 268435456;

...

Example: row 3 = x^3 - 7x^2 + 14x - 8 = (x-1)*(x-2)*(x-4).

Cf. A028361, A006125

Cf. A157963, A135950. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 20 2009]

Sequence in context: A028246 A082038 A143774 this_sequence A090452 A110439 A065602

Adjacent sequences: A158471 A158472 A158473 this_sequence A158475 A158476 A158477

tabl,sign

Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 20 2009