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A114193 Riordan array (1/(1+2xc(-2x)),xc(-2x)/(1+2xc(-2x)), c(x) the g.f. of A000108. 4
1, -2, 1, 8, -6, 1, -40, 36, -10, 1, 224, -224, 80, -14, 1, -1344, 1440, -600, 140, -18, 1, 8448, -9504, 4400, -1232, 216, -22, 1, -54912, 64064, -32032, 10192, -2184, 308, -26, 1, 366080, -439296, 232960, -81536, 20160, -3520, 416, -30, 1, -2489344, 3055104, -1697280, 639744, -176256, 35904, -5304, 540 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are A114191. Diagonal sums are A114194. Inverse of A114192.

Triangle T(n,k), read by rows, given by (-2, -2, -2, -2, -2, -2, -2, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Jan 26 2014

LINKS

Table of n, a(n) for n=0..52.

FORMULA

Riordan array ((sqrt(1+8x)-1)/(4x), (sqrt(1+8x)-1)^2/(16x)).

T(n, k) = (-2)^(n-k)*A039599(n, k) = (-2)^(n-k)*C(2*n, n-k)*(2*k+1)/(n+k+1) . - Philippe Deléham, Nov 17 2005

EXAMPLE

Triangle begins

1;

-2, 1;

8, -6, 1;

-40, 36, -10, 1;

224, -224, 80, -14, 1;

-1344, 1440, -600, 140, -18, 1;

CROSSREFS

Cf. A039599, A084938

Sequence in context: A008517 A142336 A193735 * A231846 A039683 A108084

Adjacent sequences:  A114190 A114191 A114192 * A114194 A114195 A114196

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Nov 16 2005

STATUS

approved

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Last modified February 17 22:32 EST 2018. Contains 299297 sequences. (Running on oeis4.)