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A119335 Number triangle T(n,k) = Sum_{j=0..n-k} C(k,3j)*C(n-k,3j). 8
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 11, 17, 11, 1, 1, 1, 1, 1, 1, 21, 41, 41, 21, 1, 1, 1, 1, 1, 1, 36, 81, 101, 81, 36, 1, 1, 1, 1, 1, 1, 57, 141, 201, 201, 141, 57, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,25

COMMENTS

Row sums are A119336. Product of Pascal's triangle and A119337.

LINKS

Seiichi Manyama, Rows n = 0..139, flattened

FORMULA

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

EXAMPLE

Triangle begins

1;

1, 1;

1, 1, 1;

1, 1, 1,  1;

1, 1, 1,  1,  1;

1, 1, 1,  1,  1,   1;

1, 1, 1,  2,  1,   1,  1;

1, 1, 1,  5,  5,   1,  1,  1;

1, 1, 1, 11, 17,  11,  1,  1, 1;

1, 1, 1, 21, 41,  41, 21,  1, 1, 1;

1, 1, 1, 36, 81, 101, 81, 36, 1, 1, 1;

CROSSREFS

T(2n,n) gives A119363.

Cf. A119326.

Sequence in context: A305720 A225372 A184879 * A155869 A176564 A237717

Adjacent sequences:  A119332 A119333 A119334 * A119336 A119337 A119338

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, May 14 2006

EXTENSIONS

More terms from Seiichi Manyama, Mar 12 2019

STATUS

approved

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Last modified October 19 23:44 EDT 2019. Contains 328244 sequences. (Running on oeis4.)