

A124926


Triangle read by rows: T(n,k)=binom(n,k)*r(k), where r(k) are the Riordan numbers (r(k)=A005043(k); 0<=k<=n).


1



1, 1, 0, 1, 0, 1, 1, 0, 3, 1, 1, 0, 6, 4, 3, 1, 0, 10, 10, 15, 6, 1, 0, 15, 20, 45, 36, 15, 1, 0, 21, 35, 105, 126, 105, 36, 1, 0, 28, 56, 210, 336, 420, 288, 91, 1, 0, 36, 84, 378, 756, 1260, 1296, 819, 232, 1, 0, 45, 120, 630, 1512, 3150, 4320, 4095, 2320, 603, 1, 0, 55, 165
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OFFSET

0,9


COMMENTS

Row sums = Catalan numbers, A000108: (1, 1, 2, 5, 14, 42...); e.g. sum of row 4 terms = A000108(4) = 14 = (1 + 0 + 6 + 4 + 3). A005043 is the inverse binomial transform of the Catalan numbers.


REFERENCES

ChaoJen Wang, Applications of the GouldenJackson cluster method to counting Dyck paths by occurrences of subwords, http://people.brandeis.edu/~gessel/homepage/students/wangthesis.pdf.


LINKS

Table of n, a(n) for n=0..69.


EXAMPLE

First few rows of the triangle are:
1;
1, 0;
1, 0, 1;
1, 0, 3, 1;
1, 0, 6, 4, 3;
1, 0, 10, 10, 15, 6;
1, 0, 15, 20, 45, 36, 15;
...


MAPLE

r:=n>(1/(n+1))*sum((1)^i*binomial(n+1, i)*binomial(2*n2*i, ni), i=0..n): T:=(n, k)>r(k)*binomial(n, k): for n from 0 to 11 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form


CROSSREFS

Cf. A005043, A000108.
Sequence in context: A162169 A216954 A124801 * A175946 A115378 A120060
Adjacent sequences: A124923 A124924 A124925 * A124927 A124928 A124929


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Nov 12 2006


EXTENSIONS

Edited by N. J. A. Sloane, Nov 29 2006


STATUS

approved



