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%I #9 Mar 31 2015 20:20:30
%S 0,1,1,2,3,5,3,6,15,42,4,10,34,130,514,5,15,65,315,1565,7815,6,21,111,
%T 651,3891,23331,139971,7,28,175,1204,8407,58828,411775,2882404,8,36,
%U 260,2052,16388,131076,1048580,8388612,67108868,9,45,369,3285,29529,265725
%N Triangle read by rows: T(n,k) = n*(1+n^k)/2, 0<=k<=n.
%C Row sums give A108397;
%C T(n,0) = A001477(n);
%C T(n,1) = A000217(n) for n>0;
%C T(n,2) = A006003(n) for n>1;
%C T(n,3) = A027441(n) for n>2;
%C T(n,4) = A021003(n) for n>3;
%C T(n,n) = A108398(n).
%H Reinhard Zumkeller, <a href="/A108396/b108396.txt">Rows n = 0..124 of triangle, flattened</a>
%e . 0: 0
%e . 1: 1 1
%e . 2: 2 3 5
%e . 3: 3 6 15 42
%e . 4: 4 10 34 130 514
%e . 5: 5 15 65 315 1565 7815
%e . 6: 6 21 111 651 3891 23331 139971
%e . 7: 7 28 175 1204 8407 58828 411775 2882404
%e . 8: 8 36 260 2052 16388 131076 1048580 8388612 67108868
%e . 9: 9 45 369 3285 29529 265725 2391489 21523365 193710249 1743392205 .
%t Join[{0},Flatten[Table[n (1+n^k)/2,{n,10},{k,0,n}]]] (* _Harvey P. Dale_, Mar 19 2015 *)
%o (Haskell)
%o a108396 n k = a108396_tabl !! n !! k
%o a108396_row n = a108396_tabl !! n
%o a108396_tabl = zipWith (\v ws -> map (flip div 2 . (* v) . (+ 1)) ws)
%o [0..] a079901_tabl
%o -- _Reinhard Zumkeller_, Mar 31 2015
%Y Cf. A079901, A000312, A033918, A001477, A000217, A006003, A027441, A021003, A108398, A108397 (row sums), A256512 (central terms).
%K nonn,tabl
%O 0,4
%A _Reinhard Zumkeller_, Jun 02 2005
%E Offset changed by _Reinhard Zumkeller_, Mar 31 2015
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