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A117411 Skew triangle associated to the Euler numbers. 3
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; text; internal format)
OFFSET

0,5

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 Deléham, Nov 01 2009]

LINKS

Table of n, a(n) for n=0..81.

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, Mar 14 2006

T(n,k)=(-4)^(n-k)*A098158(n,k). [From Philippe Deléham, Nov 01 2009]

T(n,k) = 2*T(n-1,k-1) - 4*T(n-2,k-1) - T(n-2,k-2), T(0,0) = T(1,1) = 1, T(1,0) = 0, T(n,k) = 0 if k>n or if k<0. - Philippe Deléham, Oct 31 2013

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

CROSSREFS

Sequence in context: A182878 A221971 A085992 * A161739 A291574 A094924

Adjacent sequences:  A117408 A117409 A117410 * A117412 A117413 A117414

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Mar 13 2006

STATUS

approved

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Last modified December 11 06:24 EST 2017. Contains 295868 sequences.