A108398 -id:A108398 - cp's OEIS frontend

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

Reinhard Zumkeller, Jun 02 2005

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).

			.  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 .

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

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

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

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

Offset changed by Reinhard Zumkeller, Mar 31 2015

A256512 n(1+(2n)^n).

Original entry on oeis.org

0, 3, 34, 651, 16388, 500005, 17915910, 737894535, 34359738376, 1785233613321, 102400000000010, 6427501315524619, 438244169232678924, 32254987351648575501, 2548827677619195478030, 215233605000000000000015, 19342813113834066795298832

Offset: 0

Reinhard Zumkeller, Mar 31 2015

nonn

a(n) = A108396(2*n,n): central terms of the triangle A108396.

Reinhard Zumkeller, Table of n, a(n) for n = 0..250

Cf. A062971, A108396, A108398.

Haskell
```
a256512 n = n * (1 + (2 * n) ^ n)
```

Join[{0},Table[n(1+(2n)^n),{n,20}]] (* Harvey P. Dale, Aug 05 2021 *)

A322406 a(n) = n + n*n^n.

Original entry on oeis.org

2, 10, 84, 1028, 15630, 279942, 5764808, 134217736, 3486784410, 100000000010, 3138428376732, 106993205379084, 3937376385699302, 155568095557812238, 6568408355712890640, 295147905179352825872, 14063084452067724991026, 708235345355337676357650, 37589973457545958193355620

Offset: 1

Ivan Stoykov, Dec 07 2018

All terms are produced by successively applying the three basic operations: exponentiation, multiplication and addition.

			a(3) = 3 + 3*3^3 = 3 + 3*27 = 8 + 81 = 84.

Muniru A Asiru, Table of n, a(n) for n = 1..380
R. L. Goodstein, Transfinite Ordinals in Recursive Number Theory, Journal of Symbolic Logic, Vol. 12, No. 4 (Dec. 1947), pp. 123-129.

Cf. A066068, A055897.

Equals 2 * A108398.

List([1..20],n->n+n*n^n); # Muniru A Asiru, Dec 07 2018

[n+n*n^n$n=1..20]; # Muniru A Asiru, Dec 07 2018

a[n_]:=n+n*n^n; Array[a, 20] (* Stefano Spezia, Dec 07 2018 *)

a(n) = n+n*n^n \\ Felix Fröhlich, Dec 07 2018

E.g.f.: exp(x) * x - LambertW(-x)/(1 + LambertW(-x))^3. - Vaclav Kotesovec, Dec 20 2018

a(12)-a(19) from Stefano Spezia, Dec 07 2018

cp's OEIS Frontend

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

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A256512 n(1+(2n)^n).

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A322406 a(n) = n + n*n^n.

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cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

Extensions

A256512 n*(1+(2*n)^n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Mathematica

A322406 a(n) = n + n*n^n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

GAP

Maple

Mathematica

PARI

Formula

Extensions

A256512 n(1+(2n)^n).