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A117317 Triangle related to partitions of n. 5
1, 2, 1, 4, 5, 1, 8, 16, 9, 1, 16, 44, 41, 14, 1, 32, 112, 146, 85, 20, 1, 64, 272, 456, 377, 155, 27, 1, 128, 640, 1312, 1408, 833, 259, 35, 1, 256, 1472, 3568, 4712, 3649, 1652, 406, 44, 1, 512, 3328, 9312, 14608, 14002, 8361, 3024, 606, 54, 1, 1024, 7424, 23552 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are A007052. Diagonal sums are A052988. Reversal of A056242.

Essentially given by (0, 2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Jan 28 2012

LINKS

Table of n, a(n) for n=0..57.

FORMULA

Number triangle T(n,k)=sum{j=0..n-k, C(n+j,k)C(n-k,j)}

T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k-1) - T(n-2,k-2) for n>1. - Philippe Deléham, Jan 28 2012

G.f.: (1-y*x)/(1-2*(y+1)*x+y*(y+1)*x^2). - Philippe Deléham, Jan 28 2012

EXAMPLE

Triangle begins

1,

2, 1,

4, 5, 1,

8, 16, 9, 1,

16, 44, 41, 14, 1,

32, 112, 146, 85, 20, 1,

64, 272, 456, 377, 155, 27, 1

Triangle (0, 2, 0, 0, 0, 0, ...) DELTA (1, 0, 1/2, 1/2, 0, 0, ...) begins :

1

0, 1

0, 2, 1

0, 4, 5, 1

0, 8, 16, 9, 1

0, 16, 44, 41, 14, 1

0, 32, 112, 146, 85, 20, 1

0, 64, 272, 456, 377, 155, 27, 1

CROSSREFS

Cf. Columns : A000079, A053220, A056243 ; Diagonals : A000012, A000096

Sequence in context: A080935 A102661 A121574 * A124237 A123876 A114164

Adjacent sequences:  A117314 A117315 A117316 * A117318 A117319 A117320

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Mar 07 2006

STATUS

approved

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Last modified April 20 05:52 EDT 2014. Contains 240779 sequences.