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A115179 Expansion of c(x*y(1-x)), c(x) the g.f. of A000108. 2
1, 0, 1, 0, -1, 2, 0, 0, -4, 5, 0, 0, 2, -15, 14, 0, 0, 0, 15, -56, 42, 0, 0, 0, -5, 84, -210, 132, 0, 0, 0, 0, -56, 420, -792, 429, 0, 0, 0, 0, 14, -420, 1980, -3003, 1430, 0, 0, 0, 0, 0, 210, -2640, 9009, -11440, 4862, 0, 0, 0, 0, 0, -42, 1980, -15015, 40040, -43758, 16796, 0, 0, 0, 0, 0, 0, -792 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Since c(x(1-x))=1/(1-x), the row sums of this triangle are (1,1,1,...). This establishes the identity sum{k=0..n, (-1)^(n-k)*C(k)*C(k,n-k)}=1. Diagonal sums are A117437. Alternating sign version of A117434.

LINKS

Table of n, a(n) for n=0..72.

FORMULA

Number triangle T(n,k)=(-1)^(n-k)*C(k)*C(k,n-k).

EXAMPLE

Triangle begins

.1,

.0, 1,

.0, -1, 2,

.0, 0, -4, 5,

.0, 0, 2, -15, 14,

.0, 0, 0, 15, -56, 42,

.0, 0, 0, -5, 84, -210, 132,

.0, 0, 0, 0, -56, 420, -792, 429

CROSSREFS

Sequence in context: A094295 A085969 A117434 * A131742 A257813 A278280

Adjacent sequences:  A115176 A115177 A115178 * A115180 A115181 A115182

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Mar 14 2006

STATUS

approved

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Last modified December 12 06:05 EST 2017. Contains 295937 sequences.