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A265848 Pascal's triangle, right and left halves interchanged.

%I A265848 #21 May 13 2025 02:40:12
%S A265848 1,1,1,1,1,2,3,1,1,3,4,1,1,4,6,10,5,1,1,5,10,15,6,1,1,6,15,20,35,21,7,
%T A265848 1,1,7,21,35,56,28,8,1,1,8,28,56,70,126,84,36,9,1,1,9,36,84,126,210,
%U A265848 120,45,10,1,1,10,45,120,210,252,462,330,165,55,11,1,1,11,55,165,330,462
%N A265848 Pascal's triangle, right and left halves interchanged.
%C A265848 Concatenations of rows of A014413 and A034868.
%C A265848 Alternative mirrored variant: concatenation of A034869 and A014462.
%H A265848 Reinhard Zumkeller, <a href="/A265848/b265848.txt">Rows n = 0..150 of triangle, flattened</a>
%H A265848 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>.
%F A265848 T(n,k) = A007318(n, (k + floor((n+2)/2)) mod (n+1)).
%F A265848 T(n,k) = if k <= [(n+1)/2] then A014413(n,k+1) else A034868(n,k-[(n+1)/2]).
%F A265848 T(n,0) = A037952(n) for n > 0.
%F A265848 T(n,n) = A001405(n).
%e A265848 .   0:                                1
%e A265848 .   1:                              1   1
%e A265848 .   2:                            1   1   2
%e A265848 .   3:                          3   1   1   3
%e A265848 .   4:                        4   1   1   4   6
%e A265848 .   5:                     10   5   1   1   5   10
%e A265848 .   6:                   15   6   1   1   6   15  20
%e A265848 .   7:                 35   21  7   1   1   7   21   35
%e A265848 .   8:              56   28   8   1   1   8   28  56   70
%e A265848 .   9:           126   84   36  9   1   1   9   36   84   126
%e A265848 .  10:        210   120  45  10   1   1   10  45  120  210  252
%e A265848 .  11:     462   330  165   55  11  1   1   11  55  165   330  462
%e A265848 .  12:  792   495  220   66  12   1   1   12  66  220  495  792   924  .
%t A265848 row[n_] := Binomial[n, Join[Range[Floor[n/2] + 1, n], Range[0, Floor[n/2]]]]; Array[row, 12, 0] // Flatten (* _Amiram Eldar_, May 13 2025 *)
%o A265848 (Haskell)
%o A265848 a265848 n k = a265848_tabl !! n !! k
%o A265848 a265848_row n = a265848_tabl !! n
%o A265848 a265848_tabl = zipWith (++) ([] : a014413_tabf) a034868_tabf
%Y A265848 Cf. A014413, A014462, A034868, A034869, A007318, A001405, A037952, A000079 (row sums), A001142 (row products).
%K A265848 nonn,tabl,easy
%O A265848 0,6
%A A265848 _Reinhard Zumkeller_, Dec 24 2015