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A186826 Riordan array (s(x),x*S(x)) where s(x) is the g.f. of the little Schroeder numbers A001003, and S(x) is the g.f. of the large Schroeder numbers A006318. 6
1, 1, 1, 3, 3, 1, 11, 11, 5, 1, 45, 45, 23, 7, 1, 197, 197, 107, 39, 9, 1, 903, 903, 509, 205, 59, 11, 1, 4279, 4279, 2473, 1061, 347, 83, 13, 1, 20793, 20793, 12235, 5483, 1949, 541, 111, 15, 1, 103049, 103049, 61463, 28435, 10717, 3285, 795, 143, 17, 1, 518859, 518859, 312761, 148249, 58351, 19199, 5197, 1117, 179, 19, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Reverse of A144944. Inverse of A186827. Row sums are A010683. Diagonal sums are A186828.

LINKS

Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

FORMULA

Riordan array ((1+x+sqrt(1-6x+x^2))/(4x), (1-x-sqrt(1-6x+x^2))/2).

R(n,k)=k*sum(i=0..n-k, (A001003(i)/(n-i))*sum(m=0..n-k-i, binomial(n-i,m)*binomial(2*(n-i)-m-k-1,n-i-1))), k>0, R(n,0)=A001003(n). [From Vladimir Kruchinin, Mar 09 2011]

EXAMPLE

Triangle begins

1,

1, 1,

3, 3, 1,

11, 11, 5, 1,

45, 45, 23, 7, 1,

197, 197, 107, 39, 9, 1,

903, 903, 509, 205, 59, 11, 1,

4279, 4279, 2473, 1061, 347, 83, 13, 1,

20793, 20793, 12235, 5483, 1949, 541, 111, 15, 1,

103049, 103049, 61463, 28435, 10717, 3285, 795, 143, 17, 1,

518859, 518859, 312761, 148249, 58351, 19199, 5197, 1117, 179, 19, 1

Production matrix of this triangle begins

1, 1,

2, 2, 1,

2, 2, 2, 1,

2, 2, 2, 2, 1,

2, 2, 2, 2, 2, 1,

2, 2, 2, 2, 2, 2, 1,

2, 2, 2, 2, 2, 2, 2, 1,

2, 2, 2, 2, 2, 2, 2, 2, 1,

2, 2, 2, 2, 2, 2, 2, 2, 2, 1

For instance, 107=1*45+2*23+2*7+2*1.

PROG

(Haskell)

a186826 n k = a186826_tabl !! n !! k

a186826_row n = a186826_tabl !! n

a186826_tabl = map reverse a144944_tabl

-- Reinhard Zumkeller, May 11 2013

CROSSREFS

Sequence in context: A131889 A292386 A174287 * A185418 A050609 A120870

Adjacent sequences:  A186823 A186824 A186825 * A186827 A186828 A186829

KEYWORD

nonn,easy,tabl

AUTHOR

Paul Barry, Feb 27 2011

STATUS

approved

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Last modified October 23 06:13 EDT 2018. Contains 316519 sequences. (Running on oeis4.)