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A117375 Riordan array (1/(1-3x*c(x)),xc(x)), c(x) the g.f. of A000108. 2
1, 3, 1, 12, 4, 1, 51, 17, 5, 1, 222, 74, 23, 6, 1, 978, 326, 104, 30, 7, 1, 4338, 1446, 468, 142, 38, 8, 1, 19323, 6441, 2103, 657, 189, 47, 9, 1, 86310, 28770, 9447, 3006, 903, 246, 57, 10, 1, 386250, 128750, 42440, 13670, 4223, 1217, 314, 68, 11, 1, 1730832 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Triangle factors as (1,xc(x))*(1/(1-3x),x). First row is A007854. Second row is A049027(n)-0^n. Row sums are A049027(n+1). Diagonal sums are A117376.

LINKS

Table of n, a(n) for n=0..55.

FORMULA

Number triangle T(0,0)=1, T(n,k)=[k<=n]*sum{j=0..n, (j/(n-j))*C(2n-j,n-j)[k<=j]*3^(j-k)}

EXAMPLE

Triangle begins

1,

3, 1,

12, 4, 1,

51, 17, 5, 1,

222, 74, 23, 6, 1,

978, 326, 104, 30, 7, 1,

4338, 1446, 468, 142, 38, 8, 1

Production array begins

3, 1

3, 1, 1

3, 1, 1, 1

3, 1, 1, 1, 1

3, 1, 1, 1, 1, 1

3, 1, 1, 1, 1, 1, 1

3, 1, 1, 1, 1, 1, 1, 1

3, 1, 1, 1, 1, 1, 1, 1, 1

... - Philippe Deléham, Mar 05 2013

CROSSREFS

Sequence in context: A287954 A287462 A287985 * A162995 A177020 A226167

Adjacent sequences:  A117372 A117373 A117374 * A117376 A117377 A117378

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Mar 10 2006

STATUS

approved

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Last modified November 19 20:42 EST 2019. Contains 329323 sequences. (Running on oeis4.)