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A108396 Triangle read by rows: T(n,k) = n*(1+n^k)/2, 0<=k<=n.

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