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A172380 Eigentriangle of Catalan triangle A033184. 3
1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 5, 10, 6, 1, 0, 14, 36, 31, 10, 1, 0, 42, 137, 156, 75, 15, 1, 0, 132, 544, 787, 510, 155, 21, 1, 0, 429, 2235, 4017, 3331, 1380, 287, 28, 1, 0, 1430, 9445, 20809, 21405, 11411, 3255, 490, 36, 1, 0, 4862, 40876, 109486, 136921, 90665 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are A091768. Production matrix of inverse is matrix with general term (-1)^(n-k+1)C(k,n-k+1).

Diagonal sums are A172382. Product of A033184 and A172380 is the matrix A172381.

LINKS

Table of n, a(n) for n=0..60.

P. Barry, Invariant number triangles, eigentriangles and Somos-4 sequences, arXiv preprint arXiv:1107.5490, 2011

EXAMPLE

Triangle begins

1,

0, 1,

0, 1, 1,

0, 2, 3, 1,

0, 5, 10, 6, 1,

0, 14, 36, 31, 10, 1,

0, 42, 137, 156, 75, 15, 1,

0, 132, 544, 787, 510, 155, 21, 1,

0, 429, 2235, 4017, 3331, 1380, 287, 28, 1,

0, 1430, 9445, 20809, 21405, 11411, 3255, 490, 36, 1

Production matrix of inverse is

0, 1,

0, -1, 1,

0, 0, -2, 1,

0, 0, 1, -3, 1,

0, 0, 0, 3, -4, 1,

0, 0, 0, -1, 6, -5, 1,

0, 0, 0, 0, -4, 10, -6, 1,

0, 0, 0, 0, 1, -10, 15, -7, 1,

0, 0, 0, 0, 0, 5, -20, 21, -8, 1,

0, 0, 0, 0, 0, -1, 15, -35, 28, -9, 1,

0, 0, 0, 0, 0, 0, -6, 35, -56, 36, -10, 1

CROSSREFS

Sequence in context: A081247 A298753 A173050 * A144633 A264428 A256550

Adjacent sequences:  A172377 A172378 A172379 * A172381 A172382 A172383

KEYWORD

nonn,tabl

AUTHOR

Paul Barry, Feb 01 2010

STATUS

approved

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Last modified February 21 02:02 EST 2020. Contains 332086 sequences. (Running on oeis4.)