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A119337 Number triangle T(n,k)=sum{i=0..n, (-1)^(n-i)*C(n,i)*sum{j=0..i-k, C(k,3j)*C(i-k,3j)}}. 1
1, 0, 1, 0, -1, 1, 0, 1, -2, 1, 0, -1, 3, -3, 1, 0, 1, -4, 6, -4, 1, 0, -1, 5, -9, 10, -5, 1, 0, 1, -6, 12, -16, 15, -6, 1, 0, -1, 7, -15, 19, -25, 21, -7, 1, 0, 1, -8, 18, -16, 20, -36, 28, -8, 1, 0, -1, 9, -21, 4, 24, 6, -49, 36, -9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Row sums have g.f. (1+x)/(1-x)^6. Multiply by Pascal's triangle A007318 to get A119335.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

Column k has g.f. (x/(1+x))^k*sum{j=0..k, C(k,3j)x^(3j)}

EXAMPLE

Triangle begins

1,

0, 1,

0, -1, 1,

0, 1, -2, 1,

0, -1, 3, -3, 1,

0, 1, -4, 6, -4, 1,

0, -1, 5, -9, 10, -5, 1,

0, 1, -6, 12, -16, 15, -6, 1,

0, -1, 7, -15, 19, -25, 21, -7, 1,

0, 1, -8, 18, -16, 20, -36, 28, -8, 1,

0, -1, 9, -21, 4, 24, 6, -49, 36, -9, 1

CROSSREFS

Sequence in context: A279594 A077593 A213888 * A213889 A110555 A097805

Adjacent sequences:  A119334 A119335 A119336 * A119338 A119339 A119340

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, May 14 2006

STATUS

approved

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Last modified October 19 21:17 EDT 2019. Contains 328229 sequences. (Running on oeis4.)