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A228643 Triangle read by rows: T(n,1) = n * (n - 1) + 1 and for k: 1 < k <= n: T(n,k) = T(n,k-1) + T(n-1,k-1).

%I A228643 #5 Aug 29 2013 14:26:56
%S A228643 1,3,4,7,10,14,13,20,30,44,21,34,54,84,128,31,52,86,140,224,352,43,74,
%T A228643 126,212,352,576,928,57,100,174,300,512,864,1440,2368,73,130,230,404,
%U A228643 704,1216,2080,3520,5888,91,164,294,524,928,1632,2848,4928,8448
%N A228643 Triangle read by rows: T(n,1) = n * (n - 1) + 1 and for k: 1 < k <= n: T(n,k) = T(n,k-1) + T(n-1,k-1).
%C A228643 T(n,1) = A002061(n); T(n,2) = A005893(n-1) for n > 1;
%C A228643 T(n,n) = A007466(n).
%H A228643 Reinhard Zumkeller, <a href="/A228643/b228643.txt">Rows n = 1..100 of table, flattened</a>
%e A228643 .   1:    1
%e A228643 .   2:    3,  4
%e A228643 .   3:    7, 10, 14
%e A228643 .   4:   13, 20, 30, 44
%e A228643 .   5:   21, 34, 54, 84, 128
%e A228643 .   6:   31, 52, 86,140, 224, 352
%e A228643 .   7:   43, 74,126,212, 352, 576, 928
%e A228643 .   8:   57,100,174,300, 512, 864,1440,2368
%e A228643 .   9:   73,130,230,404, 704,1216,2080,3520, 5888
%e A228643 .  10:   91,164,294,524, 928,1632,2848,4928, 8448,14336
%e A228643 .  11:  111,202,366,660,1184,2112,3744,6592,11520,19968,34304
%e A228643 .  12:  133,244,446,812,1472,2656,4768,8512,15104,26624,46592,80896.
%o A228643 (Haskell)
%o A228643 a228643 n k = a228643_tabl !! (n-1) !! (k-1)
%o A228643 a228643_row n = a228643_tabl !! (n-1)
%o A228643 a228643_tabl = map fst $ iterate
%o A228643    (\(row, x) -> (scanl (+) (x * (x - 1) + 1) row, x + 1)) ([1], 2)
%K A228643 nonn,tabl
%O A228643 1,2
%A A228643 _J. M. Bergot_ and _Reinhard Zumkeller_, Aug 29 2013