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A137940 Triangle read by rows, antidiagonals of an array formed by A000012 * A001263(transform). 0
1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 2, 5, 7, 1, 1, 2, 5, 13, 11, 1, 1, 2, 5, 14, 31, 16, 1, 1, 2, 5, 14, 41, 66, 22, 1, 1, 2, 5, 14, 42, 116, 127, 29, 1, 1, 2, 5, 14, 42, 131, 302, 225, 37, 1, 1, 2, 5, 14, 42, 132, 407, 715, 373, 46, 1, 1, 2, 5, 14, 42, 132 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Rows of the array tend to the Catalan sequence, A000108 starting (1, 2, 5, 14, 42,...).

LINKS

Table of n, a(n) for n=1..72.

FORMULA

Antidiagonals of an array formed by A000012 * A001263(transform), as infinite triangular matrices. A000012 = (1; 1,1; 1,1,1; 1,1,1,1;...), A001263 = the Narayana triangle.

EXAMPLE

First few rows of the array are:

1,...1,....1,....1,....1,...

1,...2,....4,....7,...11,...

1,...2,....5,...13,...31,...

1,...2,....5,...14,...41,...

1,...2,....5,...14,...42,...

...

First few rows of the triangle are:

1;

1, 1;

1, 2, 1;

1, 2, 4, 1;

1, 2, 5, 7, 1;

1, 2, 5, 13, 11, 1;

1, 2, 5, 14, 31, 16, 1;

1, 2, 5, 14, 41, 66, 22, 1;

1, 2, 5, 14, 42, 116, 127, 29, 1;

1, 2, 5, 14, 42, 131, 302, 225, 37, 1;

1, 2, 5, 14, 42, 132, 407, 715, 373, 46, 1;

...

CROSSREFS

Cf. A001263, A000108.

Sequence in context: A245163 A140993 A027935 * A274859 A137855 A113143

Adjacent sequences:  A137937 A137938 A137939 * A137941 A137942 A137943

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Feb 24 2008

STATUS

approved

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Last modified September 20 22:20 EDT 2019. Contains 327252 sequences. (Running on oeis4.)