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A158474
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Triangle read by rows generated from (x-1)*(x-2)*(x-4)*...
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6
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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, 4161536, -2097152, 1, -255, 21590, -777240, 12850368, -99486720, 353730560
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sum of the unsigned triangle = A028361: (1, 2, 6, 30, 270, 4590,...). Right border of the unsigned 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]
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FORMULA
| T(n,k) = coefficient [x^(n-k)] of (x-1)*(x-2)*(x-4)*...*(x-2^(n-1)).
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EXAMPLE
| First few rows of the 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).
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MAPLE
| A158474 := proc(n, k) mul(x-2^j, j=0..n-1) ; expand(%); coeftayl(%, x=0, n-k) ; end proc: # R. J. Mathar, Aug 27 2011
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CROSSREFS
| Cf. A028361, A006125
Cf. A157963, A135950. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 20 2009]
Sequence in context: A082038 A143774 A196842 * A090452 A193924 A110439
Adjacent sequences: A158471 A158472 A158473 * A158475 A158476 A158477
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KEYWORD
| tabl,sign
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 20 2009
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