A247023 Riordan array (1/(1-2*x), x*C(x)) where C(x) is the o.g.f. of Catalan numbers A000108.

1, 2, 1, 4, 3, 1, 8, 8, 4, 1, 16, 21, 13, 5, 1, 32, 56, 40, 19, 6, 1, 64, 154, 122, 66, 26, 7, 1, 128, 440, 376, 222, 100, 34, 8, 1, 256, 1309, 1181, 741, 365, 143, 43, 9, 1, 512, 4048, 3792, 2483, 1302, 561, 196, 53, 10, 1, 1024, 12958, 12446, 8398, 4606

Offset: 0

Author

Philippe Deléham, Sep 13 2014

Keywords

• nonn
• tabl

Comments

Row sums are A014318.

Mirror image of the triangle in A201634.

Examples

			Triangle begins
1
2, 1
4, 3, 1
8, 8, 4, 1
16, 21, 13, 5, 1
32, 56, 40, 19, 6, 1
64, 154, 122, 66, 26, 7, 1
Production matrix begins
2, 1
0, 1, 1
0, 1, 1, 1
0, 1, 1, 1, 1
0, 1, 1, 1, 1, 1
0, 1, 1, 1, 1, 1, 1
0, 1, 1, 1, 1, 1, 1, 1
		

Links

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

Crossrefs

Cf. A000079, A000108, A014318, A201634.

Programs

Haskell

a247023 n k = a247023_tabl !! n !! k
a247023_row n = a247023_tabl !! n
a247023_tabl = map reverse a201634_tabl
-- Reinhard Zumkeller, Sep 20 2014

Formula

T(n,0) = 2^n = A000079(n).

T(n+1,1) = A014318(n).

Extensions

Data corrected by Reinhard Zumkeller, Sep 20 2014