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A108396 Triangle read by rows: T(n,k) = n*(1+n^k)/2, 0<=k<=n. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 3 11:40 EST 2023. Contains 360034 sequences. (Running on oeis4.)