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A154380 The Riordan square of the Bell numbers. Triangle T(n, k), 0 <= k <= n, read by rows. 3
1, 1, 1, 2, 3, 1, 5, 9, 5, 1, 15, 29, 20, 7, 1, 52, 102, 77, 35, 9, 1, 203, 392, 302, 157, 54, 11, 1, 877, 1641, 1235, 683, 277, 77, 13, 1, 4140, 7451, 5324, 2987, 1329, 445, 104, 15, 1, 21147, 36525, 24329, 13391, 6230, 2340, 669, 135, 17, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The Riordan square is defined in A321620.

Previous name was: Triangle T(n,k), 0<=k<=n, read by rows given by [1, 1, 1, 2, 1, 3, 1, 4, 1, ...] DELTA [1, 0, 0, 0, ...] where DELTA is the operator defined in A084938.

In general, the triangle [r_0, r_1, r_2, ...] DELTA [s_0, s_1, s_2, ...] has generating function

1/(1 - (r_0*x + s_0*x*y)/(1 - (r_1*x + s_1*x*y)/(1 - (r_2*x + s_2*x*y)/(1 -... (continued fraction)

A130167*A007318 as infinite lower triangular matrices. - Philippe Deléham, Jan 11 2009

LINKS

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

P. Barry, Continued fractions and transformations of integer sequences, JIS 12 (2009) 09.7.6.

FORMULA

G.f.: 1/(1-(x+xy)/(1-x/(1-x/(1-2x/(1-x/(1-3x/(1-x/(1-4x/(1-... (continued fraction).

EXAMPLE

Triangle begins

     1;

     1,   1;

     2,   3,   1;

     5,   9,   5,   1;

    15,  29,  20,   7,  1;

    52, 102,  77,  35,  9,  1;

   203, 392, 302, 157, 54, 11, 1;

MAPLE

# The function RiordanSquare is defined in A321620.

RiordanSquare(add(x^k/mul(1-j*x, j=1..k), k=0..10), 10); # Peter Luschny, Dec 06 2018

CROSSREFS

First column are the Bell numbers A000110.

Row sums are A154381, alternating row sums are A000007.

Cf. A321620.

Sequence in context: A147703 A147747 A039599 * A155083 A011357 A080409

Adjacent sequences:  A154377 A154378 A154379 * A154381 A154382 A154383

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jan 08 2009

EXTENSIONS

New name by Peter Luschny, Dec 06 2018

STATUS

approved

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Last modified January 18 11:28 EST 2019. Contains 319271 sequences. (Running on oeis4.)