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 A117317 Triangle related to partitions of n. 6
 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 Reinhard Zumkeller, Rows n = 0..125 of table, flattened 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 PROG (Haskell) a117317 n k = a117317_tabl !! n !! k a117317_row n = a117317_tabl !! n a117317_tabl = map reverse a056242_tabl -- Reinhard Zumkeller, May 08 2014 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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