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A153585 Convolution triangle, A053121 * (A001405 * 0^(n-k)) 3
1, 0, 1, 1, 0, 2, 0, 2, 0, 3, 2, 0, 6, 0, 6, 0, 5, 0, 12, 0, 10, 5, 0, 18, 0, 30, 0, 20, 0, 14, 0, 42, 0, 60, 0, 35, 14, 0, 56, 0, 120, 0, 140, 0, 70, 0, 42, 0, 144, 0, 270, 0, 280, 0, 126 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Row sums = A145974: (1, 1, 3, 5, 14, 27, 73,...).

LINKS

Table of n, a(n) for n=0..54.

FORMULA

Convolution triangle, A053121 * (A001405 * 0^(n-k)).

A053121 = the aerated Catalan triangle and (A001405 * 0^(n-k) = an

infinite lower triangular matrix with A001405 as the main diagonal and

the rest zeros.

EXAMPLE

First few rows of the triangle =

1;

0, 1;

1, 0, 2;

0, 2, 0, 3;

2, 0, 6, 0, 6;

0, 5, 0, 12, 0, 10;

5, 0, 18, 0, 30, 0, 20;

0, 14, 0, 42, 0, 60, 0, 35;

14, 0, 56, 0, 120, 0, 140, 0, 70;

0, 42, 0, 144, 0, 270, 0, 280, 0, 126;

42, 0, 180, 0, 450, 0, 700, 0, 630, 0, 252;

...

Example: Row 4 = (2, 0, 6, 0, 6) = termwise products of (2, 0, 3, 0, 1) and (1, 1, 2, 3, 6).

CROSSREFS

Sequence in context: A029224 A029188 A090290 * A169611 A242460 A144494

Adjacent sequences:  A153582 A153583 A153584 * A153586 A153587 A153588

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Dec 28 2008

STATUS

approved

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Last modified November 27 04:09 EST 2014. Contains 250155 sequences.