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A117411
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Skew triangle associated to the Euler numbers.
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3
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1, 0, 1, 0, -4, 1, 0, 0, -12, 1, 0, 0, 16, -24, 1, 0, 0, 0, 80, -40, 1, 0, 0, 0, -64, 240, -60, 1, 0, 0, 0, 0, -448, 560, -84, 1, 0, 0, 0, 0, 256, -1792, 1120, -112, 1, 0, 0, 0, 0, 0, 2304, -5376, 2016, -144, 1, 0, 0, 0, 0, 0, -1024, 11520, -13440, 3360, -180, 1, 0, 0, 0, 0, 0, 0, -11264, 42240, -29568, 5280, -220, 1, 0, 0, 0, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are A006495 (binomial transform of (1,0,-4,0,16,0,-32,...)). Diagonal sums are A117413. Inverse is A117414. Row sums of the inverse are the Euler numbers A000364.
Triangle, read by rows, given by [0,-4,4,0,0,0,0,0,0,0,...] DELTA [1,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 01 2009]
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FORMULA
| Number triangle T(n,k)=sum{j=0..n-k, C(n,k-j)*C(j,n-k)}*(-4)^(n-k)
G.f.: (1-x*y)/(1-2x*y+x^2*y(y+4)); - Paul Barry (pbarry(AT)wit.ie), Mar 14 2006
T(n,k)=(-4)^(n-k)*A098158(n,k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 01 2009]
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EXAMPLE
| Triangle begins
1,
0, 1,
0, -4, 1,
0, 0, -12, 1,
0, 0, 16, -24, 1,
0, 0, 0, 80, -40, 1,
0, 0, 0, -64, 240, -60, 1,
0, 0, 0, 0, -448, 560, -84, 1,
0, 0, 0, 0, 256, -1792, 1120, -112, 1,
0, 0, 0, 0, 0, 2304, -5376, 2016, -144, 1,
0, 0, 0, 0, 0, -1024, 11520, -13440, 3360, -180, 1,
0, 0, 0, 0, 0, 0, -11264, 42240, -29568, 5280, -220, 1,
0, 0, 0, 0, 0, 0, 4096, -67584, 126720, -59136, 7920, -264, 1
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CROSSREFS
| Sequence in context: A049763 A182878 A085992 * A161739 A094924 A056968
Adjacent sequences: A117408 A117409 A117410 * A117412 A117413 A117414
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 13 2006
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