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%I #19 Mar 09 2023 22:10:53
%S 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,
%T 155,27,1,128,640,1312,1408,833,259,35,1,256,1472,3568,4712,3649,1652,
%U 406,44,1,512,3328,9312,14608,14002,8361,3024,606,54,1,1024,7424,23552
%N Triangle related to partitions of n.
%C Row sums are A007052. Diagonal sums are A052988. Reversal of A056242.
%C 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
%H Reinhard Zumkeller, <a href="/A117317/b117317.txt">Rows n = 0..125 of table, flattened</a>
%F Number triangle T(n,k)=sum{j=0..n-k, C(n+j,k)C(n-k,j)}
%F 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
%F G.f.: (1-y*x)/(1-2*(y+1)*x+y*(y+1)*x^2). - _Philippe Deléham_, Jan 28 2012
%e Triangle begins
%e 1,
%e 2, 1,
%e 4, 5, 1,
%e 8, 16, 9, 1,
%e 16, 44, 41, 14, 1,
%e 32, 112, 146, 85, 20, 1,
%e 64, 272, 456, 377, 155, 27, 1
%e Triangle (0, 2, 0, 0, 0, 0, ...) DELTA (1, 0, 1/2, 1/2, 0, 0, ...) begins :
%e 1
%e 0, 1
%e 0, 2, 1
%e 0, 4, 5, 1
%e 0, 8, 16, 9, 1
%e 0, 16, 44, 41, 14, 1
%e 0, 32, 112, 146, 85, 20, 1
%e 0, 64, 272, 456, 377, 155, 27, 1
%o (Haskell)
%o a117317 n k = a117317_tabl !! n !! k
%o a117317_row n = a117317_tabl !! n
%o a117317_tabl = map reverse a056242_tabl
%o -- _Reinhard Zumkeller_, May 08 2014
%Y Cf. Columns : A000079, A053220, A056243 ; Diagonals : A000012, A000096
%K easy,nonn,tabl
%O 0,2
%A _Paul Barry_, Mar 07 2006
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