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

0, 1, 1, 2, 3, 5, 3, 6, 15, 42, 4, 10, 34, 130, 514, 5, 15, 65, 315, 1565, 7815, 6, 21, 111, 651, 3891, 23331, 139971, 7, 28, 175, 1204, 8407, 58828, 411775, 2882404, 8, 36, 260, 2052, 16388, 131076, 1048580, 8388612, 67108868, 9, 45, 369, 3285, 29529, 265725

Offset

0,4

Comments

Row sums give A108397;

T(n,0) = A001477(n);

T(n,1) = A000217(n) for n>0;

T(n,2) = A006003(n) for n>1;

T(n,3) = A027441(n) for n>2;

T(n,4) = A021003(n) for n>3;

T(n,n) = A108398(n).

Links

Reinhard Zumkeller, Rows n = 0..124 of triangle, flattened

Example

.  0:  0
.  1:  1  1
.  2:  2  3   5
.  3:  3  6  15   42
.  4:  4 10  34  130   514
.  5:  5 15  65  315  1565   7815
.  6:  6 21 111  651  3891  23331  139971
.  7:  7 28 175 1204  8407  58828  411775  2882404
.  8:  8 36 260 2052 16388 131076 1048580  8388612  67108868
.  9:  9 45 369 3285 29529 265725 2391489 21523365 193710249 1743392205 .

Mathematica

Join[{0}, Flatten[Table[n (1+n^k)/2, {n, 10}, {k, 0, n}]]] (* Harvey P. Dale, Mar 19 2015 *)

Prog

(Haskell)
a108396 n k = a108396_tabl !! n !! k
a108396_row n = a108396_tabl !! n
a108396_tabl = zipWith (\v ws -> map (flip div 2 . (* v) . (+ 1)) ws)
                       [0..] a079901_tabl
-- Reinhard Zumkeller, Mar 31 2015

Crossrefs

Cf. A079901, A000312, A033918, A001477, A000217, A006003, A027441, A021003, A108398, A108397 (row sums), A256512 (central terms).

Sequence in context: A103781 A095244 A147593 * A239476 A117367 A080184

Adjacent sequences: A108393 A108394 A108395 * A108397 A108398 A108399

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Jun 02 2005

Extensions

Offset changed by Reinhard Zumkeller, Mar 31 2015

Status

approved