

A214281


Triangle by rows, row n contains the ConvOffs transform of the first n terms of 1, 1, 3, 2, 5, 3, 7,... (A026741 without leading zero).


3



1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 2, 6, 2, 1, 1, 5, 10, 10, 5, 1, 1, 3, 15, 10, 15, 3, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 4, 28, 28, 70, 28, 28, 4, 1, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 1, 5, 45, 60, 210, 126, 210, 60, 45, 5, 1, 1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1
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OFFSET

0,8


COMMENTS

The ConvOffs transform of a sequence s(0), s(1),..., s(t1) is defined by a(0)=1 and a(n)=a(n1)*s(tn)/s(n1) for 1<=n<t. An example of this process is also shown in the Narayana triangle, A001263. By increasing the length t of the input sequence (here: A026741) we create more and more rows of the triangle.


LINKS

Table of n, a(n) for n=0..77.
Tom Edgar and Michael Z. Spivey, Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6.


FORMULA

T(n,k) = binomial(n,k) if n is odd.


EXAMPLE

First few rows of the triangle =
1;
1, 1;
1, 1, 1;
1, 3, 3, 1;
1, 2, 6, 2, 1;
1, 5, 10, 10, 5, 1;
1, 3, 15, 10, 15, 3, 1;
1, 7, 21, 35, 35, 21, 7, 1;
1, 4, 28, 28, 70, 28, 28, 4, 1;
1, 9, 36, 84, 126, 126, 84, 36, 9, 1;
1, 5, 45, 60, 210, 126, 210, 60, 45, 5, 1;
1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1;
...


CROSSREFS

Cf. A134683 (row sums), A026741, A001263
Sequence in context: A330958 A327186 A021306 * A125300 A303992 A126717
Adjacent sequences: A214278 A214279 A214280 * A214282 A214283 A214284


KEYWORD

nonn,tabl,easy


AUTHOR

Gary W. Adamson, Jul 09 2012


STATUS

approved



