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A154380 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. 2
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

First column is A000110. Row sums are A154381.

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 . [From Philippe Deléham, Jan 11 2009]

LINKS

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

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

CROSSREFS

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

STATUS

approved

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Last modified October 20 12:34 EDT 2018. Contains 316379 sequences. (Running on oeis4.)