A008788 -id:A008788 - cp's OEIS frontend

A007778 a(n) = n^(n+1).

0, 1, 8, 81, 1024, 15625, 279936, 5764801, 134217728, 3486784401, 100000000000, 3138428376721, 106993205379072, 3937376385699289, 155568095557812224, 6568408355712890625, 295147905179352825856, 14063084452067724991009, 708235345355337676357632

Offset: 0

N. J. A. Sloane

Number of edges of the complete bipartite graph of order n+n^n, K_n,n^n. - Roberto E. Martinez II, Jan 07 2002
All rational solutions to the equation x^y = y^x, with x < y, are given by x = A000169(n+1)/A000312(n), y = A000312(n+1)/A007778(n), where n >= 1. - Nick Hobson, Nov 30 2006
a(n) is also the number of ways of writing an n-cycle as the product of n+1 transpositions. - Nikos Apostolakis, Nov 22 2008
a(n) is the total number of elements whose preimage is the empty set summed over all partial functions from [n] into [n]. - Geoffrey Critzer, Jan 12 2022

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 67.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Nick Hobson, Exponential equation.
Yidong Sun and Jujuan Zhuang, lambda-factorials of n, arXiv:1007.1339 [math.CO], 2010. - _Peter Luschny_, Jul 09 2010

Cf. A000169, A000272, A000312, A007830, A008785, A008786, A008787, A008788, A008789, A008790, A008791, A135608.
Essentially the same as A065440.
Cf. A061250, A143857. [From Reinhard Zumkeller, Jul 23 2010]

[n^(n+1):n in [0..20]]; // Vincenzo Librandi, Jan 03 2012

seq( n^(n+1), n=0..20); # G. C. Greubel, Mar 05 2020

Table[n^(n+1), {n,0,20}] (* Vladimir Joseph Stephan Orlovsky, Oct 01 2008 *)

A007778[n]:=n^(n+1)$
makelist(A007778[n],n,0,30); /* Martin Ettl, Oct 29 2012 */

vector(21, n, my(m=n-1); m^(m+1)) \\ G. C. Greubel, Mar 05 2020

[n^(n+1) for n in (0..20)] # G. C. Greubel, Mar 05 2020

E.g.f.: -W(-x)/(1 + W(-x))^3, W(x) Lambert's function (principal branch).
a(n) = Sum_{k=0..n} binomial(n,k)*A000166(k+1)*(n+1)^(n-k). - Peter Luschny, Jul 09 2010
See A008517 and A134991 for similar e.g.f.s. and A048993. - Tom Copeland, Oct 03 2011
E.g.f.: d/dx {x/(T(x)*(1-T(x)))}, where T(x) = Sum_{n >= 1} n^(n-1)*x^n/n! is the tree function of A000169. - Peter Bala, Aug 05 2012
a(n) = n*A000312(n). - R. J. Mathar, Jan 12 2017
Sum_{n>=2} 1/a(n) = A135608. - Amiram Eldar, Nov 17 2020

A003992 Square array read by upwards antidiagonals: T(n,k) = n^k for n >= 0, k >= 0.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 4, 1, 0, 1, 4, 9, 8, 1, 0, 1, 5, 16, 27, 16, 1, 0, 1, 6, 25, 64, 81, 32, 1, 0, 1, 7, 36, 125, 256, 243, 64, 1, 0, 1, 8, 49, 216, 625, 1024, 729, 128, 1, 0, 1, 9, 64, 343, 1296, 3125, 4096, 2187, 256, 1, 0, 1, 10, 81, 512, 2401, 7776, 15625, 16384, 6561, 512, 1, 0

Offset: 0

Marc LeBrun

If the array is transposed, T(n,k) is the number of oriented rows of n colors using up to k different colors. The formula would be T(n,k) = [n==0] + [n>0]*k^n. The generating function for column k would be 1/(1-k*x). For T(3,2)=8, the rows are AAA, AAB, ABA, ABB, BAA, BAB, BBA, and BBB. - Robert A. Russell, Nov 08 2018

T(n,k) is the number of multichains of length n from {} to [k] in the Boolean lattice B_k. - Geoffrey Critzer, Apr 03 2020

			Rows begin:
[1, 0,  0,   0,    0,     0,      0,      0, ...],
[1, 1,  1,   1,    1,     1,      1,      1, ...],
[1, 2,  4,   8,   16,    32,     64,    128, ...],
[1, 3,  9,  27,   81,   243,    729,   2187, ...],
[1, 4, 16,  64,  256,  1024,   4096,  16384, ...],
[1, 5, 25, 125,  625,  3125,  15625,  78125, ...],
[1, 6, 36, 216, 1296,  7776,  46656, 279936, ...],
[1, 7, 49, 343, 2401, 16807, 117649, 823543, ...], ...

T. D. Noe, Rows n = 0..50 of triangle, flattened

Rows 0-49 are A000007, A000012, A000079, A000244, A000302, A000351, A000400, A000420, A001018, A001019, A011557, A001020, A001021, A001022, A001023, A001024, A001025, A001026, A001027, A001029, A009964-A009992, A087752.
Columns 0-26 are A000012, A001477, A000290, A000578, A000583, A000584, A001014, A001015, A001016, A001017, A008454, A008455, A008456, A010801-A010813, A089081.
Main diagonal is A000312. Other diagonals include A000169, A007778, A000272, A008788. Antidiagonal sums are in A026898.
Cf. A099555.
Transpose is A004248. See A051128, A095884, A009999 for other versions.
Cf. A277504 (unoriented), A293500 (chiral).

[[(n-k)^k: k in [0..n]]: n in [0..10]]; // G. C. Greubel, Nov 08 2018

Table[If[k == 0, 1, (n - k)^k], {n, 0, 11}, {k, 0, n}]//Flatten

T(n,k) = (n-k)^k \\ Charles R Greathouse IV, Feb 07 2017

E.g.f.: Sum T(n,k)*x^n*y^k/k! = 1/(1-x*exp(y)). - Paul D. Hanna, Oct 22 2004

E.g.f.: Sum T(n,k)*x^n/n!*y^k/k! = e^(x*e^y). - Franklin T. Adams-Watters, Jun 23 2006

More terms from David W. Wilson

Edited by Paul D. Hanna, Oct 22 2004

A089072 Triangle read by rows: T(n,k) = k^n, n >= 1, 1 <= k <= n.

Original entry on oeis.org

1, 1, 4, 1, 8, 27, 1, 16, 81, 256, 1, 32, 243, 1024, 3125, 1, 64, 729, 4096, 15625, 46656, 1, 128, 2187, 16384, 78125, 279936, 823543, 1, 256, 6561, 65536, 390625, 1679616, 5764801, 16777216, 1, 512, 19683, 262144, 1953125, 10077696, 40353607, 134217728, 387420489

Offset: 1

Alford Arnold, Dec 04 2003

T(n, k) = number of mappings from an n-element set into a k-element set. - Clark Kimberling, Nov 26 2004
Let S be the semigroup of (full) transformations on [n].  Let a be in S with rank(a) = k.  Then T(n,k) = |a S|, the number of elements in the right principal ideal generated by a. - Geoffrey Critzer, Dec 30 2021
From Manfred Boergens, Jun 23 2024: (Start)
In the following two comments the restriction k<=n can be lifted, allowing all k>=1.
T(n,k) is the number of n X k binary matrices with row sums = 1.
T(n,k) is the number of coverings of [n] by tuples (A_1,...,A_k) in P([n])^k with disjoint A_j, with P(.) denoting the power set.
For nonempty A_j see A019538.
For tuples with "disjoint" dropped see A092477.
For tuples with nonempty A_j and with "disjoint" dropped see A218695. (End)

			Triangle begins:
  1;
  1,  4;
  1,  8,  27;
  1, 16,  81,  256;
  1, 32, 243, 1024,  3125;
  1, 64, 729, 4096, 15625, 46656;
  ...

Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened
Mohammad K. Azarian, Remarks and Conjectures Regarding Combinatorics of Discrete Partial Functions, Int'l Math. Forum (2022) Vol. 17, No. 3, 129-141. See Theorem 2.1(ii).

Related to triangle of Eulerian numbers A008292.
Cf. A000312, A007778, A008788, A031971 (row sums), A062206, A083282.
Cf. A085524, A085526, A120485, A226065, A352981, A252982.
Cf. A019538, A092477, A218695.

a089072 = flip (^)
a089072_row n = map (a089072 n) [1..n]
a089072_tabl = map a089072_row [1..]  -- Reinhard Zumkeller, Mar 18 2013

[k^n: k in [1..n], n in [1..12]]; // G. C. Greubel, Nov 01 2022

Column[Table[k^n, {n, 8}, {k, n}], Center] (* Alonso del Arte, Nov 14 2011 *)

flatten([[k^n for k in range(1,n+1)] for n in range(1,12)]) # G. C. Greubel, Nov 01 2022

Sum_{k=1..n} T(n, k) = A031971(n).
T(n, n) = A000312(n).
T(2*n, n) = A062206(n).
a(n) = (n + T*(1-T)/2)^T, where T = round(sqrt(2*n),0). - Gerald Hillier, Apr 12 2015
T(n,k) = A051129(n,k). - R. J. Mathar, Dec 10 2015
T(n,k) = Sum_{i=0..k} Stirling2(n,i)*binomial(k,i)*i!. - Geoffrey Critzer, Dec 30 2021
From G. C. Greubel, Nov 01 2022: (Start)
T(n, n-1) = A007778(n-1), n >= 2.
T(n, n-2) = A008788(n-2), n >= 3.
T(2*n+1, n) = A085526(n).
T(2*n-1, n) = A085524(n).
T(2*n-1, n-1) = A085526(n-1), n >= 2.
T(3*n, n) = A083282(n).
Sum_{k=1..n} (-1)^k * T(n, k) = (-1)^n * A120485(n).
Sum_{k=1..floor(n/2)} T(n-k, k) = A226065(n).
Sum_{k=1..floor(n/2)} T(n, k) = A352981(n).
Sum_{k=1..floor(n/3)} T(n, k) = A352982(n). (End)

More terms and better definition from Herman Jamke (hermanjamke(AT)fastmail.fm), Jul 10 2004

Offset corrected by Reinhard Zumkeller, Mar 18 2013

A007830 a(n) = (n+3)^n.

Original entry on oeis.org

1, 4, 25, 216, 2401, 32768, 531441, 10000000, 214358881, 5159780352, 137858491849, 4049565169664, 129746337890625, 4503599627370496, 168377826559400929, 6746640616477458432, 288441413567621167681, 13107200000000000000000, 630880792396715529789561

Offset: 0

Peter J. Cameron, Mar 15 1996

a(n-2) is the number of trees with n+1 unlabeled vertices and n labeled edges for n > 1. - Christian G. Bower, 12/99 [corrected by Jonathan Vos Post, Sep 22 2012]
a(n) is the number of nonequivalent primitive meromorphic functions with one pole of order n+3 on a Riemann surface of genus 0. - Noam Katz (noamkj(AT)hotmail.com), Mar 30 2001
Pikhurko writes: "Cameron demonstrated that the total number of edge-labeled trees with n >= 2 edges is (n+1)^(n-2) by showing that the number of vertex-labeled trees of size n is n+1 times larger than the number of edge-labeled ones." - Jonathan Vos Post, Sep 22 2012
With offset 1, a(n) is the number of ways to build a rooted labeled forest with some (possibly all or none) of the nodes from {1,2,...,n} and then build another forest with the remaining nodes. - Geoffrey Critzer, May 10 2013

M. Shapiro, B. Shapiro and A. Vainshtein - Ramified coverings of S^2 with one degenerate branching point and enumeration of edge-ordered graphs, Amer. Math. Soc. Transl., Vol. 180 (1997), pp. 219-227.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.27.

T. D. Noe, Table of n, a(n) for n = 0..100
Christian Brouder, William J. Keith, and Ângela Mestre, Closed forms for a multigraph enumeration, arXiv preprint arXiv:1301.0874 [math.CO], 2013-2015.
P. J. Cameron, Two-graphs and Trees, Discrete Math. 127 (1994) 63-74.
P. J. Cameron, Counting two-graphs related to trees, Elec. J. Combin., Vol. 2, #R4.
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
Vsevolod Gubarev, Rota-Baxter operators on a sum of fields, arXiv:1811.08219 [math.RA], 2018.
Oleg Pikhurko, Generating Edge-Labeled Trees, American Math. Monthly, 112 (2005) 919-921.
M. Shapiro, B. Shapiro and A. Vainshtein, Ramified coverings of S^2 with one degenerate branching point and enumeration of edge-ordered graphs, 1996.
Index entries for sequences related to trees

Cf. A000169, A000272, A000312, A007778.

Cf. A008785, A008786, A008787, A008788, A008789, A008790, A008791.

[(n+3)^n: n in [0..20]]; // G. C. Greubel, Mar 06 2020

A007830:=n->(n+3)^n; seq(A007830(n), n=0..20);
T := -LambertW(-x): ser := series(exp(3*T)/(1-T), x, 20):
seq(n!*coeff(ser, x, n), n = 0..18); # Peter Luschny, Jan 20 2023

Mathematica
```
Table[(n+3)^n, {n, 0, 18}]
```

a(n)=(n+3)^n \\ Charles R Greathouse IV, Feb 06 2017

[(n+3)^n for n in (0..20)] # G. C. Greubel, Mar 06 2020

E.g.f. for b(n) = a(n-3): T(x) - (3/4)*T^2(x) + (1/6)*T^3(x), where T(x) is Euler's tree function (see A000169). - Len Smiley, Nov 17 2001
E.g.f.: -LambertW(-x)^3/(x^3 * (1+LambertW(-x))). - Vladeta Jovovic, Nov 07 2003
With offset 1: E.g.f.: exp(T(x))^2/2 where T(x) is the e.g.f. for A000169. - Geoffrey Critzer, May 10 2013
E.g.f.: (1/2)*d/dx (LambertW(-x)/(-x))^2. - Wolfdieter Lang, Oct 25 2022

More terms from Wesley Ivan Hurt, May 05 2014

A008785 a(n) = (n+4)^n.

Original entry on oeis.org

1, 5, 36, 343, 4096, 59049, 1000000, 19487171, 429981696, 10604499373, 289254654976, 8649755859375, 281474976710656, 9904578032905937, 374813367582081024, 15181127029874798299, 655360000000000000000, 30041942495081691894741, 1457498964228107529355264

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. A000169, A000272, A000312, A007778, A007830, A008786, A008787, A008788, A008789, A008790, A008791.

List([0..20], n-> (n+4)^n); # G. C. Greubel, Sep 11 2019

[(n+4)^n: n in [0..20]]; // Vincenzo Librandi, Jun 11 2013

Table[(n+4)^n,{n,0,20}] (* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

vector(20, n, (n+3)^(n-1)) \\ G. C. Greubel, Nov 09 2017

[(n+4)^n for n in (0..20)] # G. C. Greubel, Sep 11 2019

E.g.f.(x) for b(n) = n^(n-4) = a(n-4): T - (7/8)*T^2 + (11/36)*T^3 - (1/24)*T^4, where T = T(x) is Euler's tree function (see A000169). - Len Smiley, Nov 17 2001
E.g.f.: LambertW(-x)^4/(x^4*(1+LambertW(-x))). - Vladeta Jovovic, Nov 07 2003
E.g.f.: (1/3)*d/dx(LambertW(-x)/(-x))^3. - Wolfdieter Lang, Oct 25 2022

A008791 a(n) = n^(n+5).

Original entry on oeis.org

0, 1, 128, 6561, 262144, 9765625, 362797056, 13841287201, 549755813888, 22876792454961, 1000000000000000, 45949729863572161, 2218611106740436992, 112455406951957393129, 5976303958948914397184, 332525673007965087890625

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Cf. A000169, A000272, A000312, A007778, A007830, A008785, A008786, A008787, A008788, A008789, A008790.

List([0..20], n-> n^(n+5)); # G. C. Greubel, Sep 11 2019

[n^(n+5): n in [0..20]]; // Vincenzo Librandi, Jun 11 2013

a:=n->mul( n, k=-4..n): seq(a(n), n=0..20); # Zerinvary Lajos, Jan 26 2008

Table[n^(n+5),{n,0,20}] (* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

vector(20, n, (n-1)^(n+4)) \\ G. C. Greubel, Sep 11 2019

[n^(n+5) for n in (0..20)] # G. C. Greubel, Sep 11 2019

E.g.f.(x): T*(1 + 52*T + 328*T^2 + 444*T^3 + 120*T^4)*(1-T)^(-11); where T=T(x) is Euler's tree function (see A000169). - Len Smiley, Nov 17 2001
See A008517 and A134991 for similar e.g.f.s and diagonals of A048993. - Tom Copeland, Oct 03 2011
E.g.f.: d^5/dx^5 {x^5/(T(x)^5*(1-T(x)))}, where T(x) = Sum_{n>=1} n^(n-1)*x^n/n! is the tree function of A000169. - Peter Bala, Aug 05 2012

A008789 a(n) = n^(n+3).

Original entry on oeis.org

0, 1, 32, 729, 16384, 390625, 10077696, 282475249, 8589934592, 282429536481, 10000000000000, 379749833583241, 15407021574586368, 665416609183179841, 30491346729331195904, 1477891880035400390625, 75557863725914323419136

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Cf. A000169, A000272, A000312, A007778, A007830, A008785, A008786, A008787, A008788, A008790, A008791.

List([0..20], n-> n^(n+3)); # G. C. Greubel, Sep 11 2019

[n^(n+3): n in [0..20]]; // Vincenzo Librandi, Jun 11 2013

printlevel := -1; a := [0]; T := x->-LambertW(-x); f := series((T(x)*(1+8*T(x)+6*(T(x))^2)/(1-T(x))^7),x,24); for m from 1 to 23 do a := [op(a),op(2*m-1,f)*m! ] od; print(a); # Len Smiley, Nov 19 2001

Table[n^(n+3),{n,0,20}](* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

vector(20, n, (n-1)^(n+2)) \\ G. C. Greubel, Sep 11 2019

[n^(n+3) for n in (0..20)] # G. C. Greubel, Sep 11 2019

E.g.f.(x): T*(1 +8*T +6*T^2)*(1-T)^(-7); where T=T(x) is Euler's tree function (see A000169). - Len Smiley, Nov 19 2001
See A008517 and A134991 for similar e.g.f.s and diagonals of A048993. - Tom Copeland, Oct 03 2011
E.g.f.: d^3/dx^3 {x^3/(T(x)^3*(1-T(x)))}, where T(x) = Sum_{n>=1} n^(n-1)*x^n/n! is the tree function of A000169. - Peter Bala, Aug 05 2012
a(n) = n*A008788(n). - R. J. Mathar, Oct 31 2015

A008786 a(n) = (n+5)^n.

Original entry on oeis.org

1, 6, 49, 512, 6561, 100000, 1771561, 35831808, 815730721, 20661046784, 576650390625, 17592186044416, 582622237229761, 20822964865671168, 799006685782884121, 32768000000000000000, 1430568690241985328321, 66249952919459433152512, 3244150909895248285300369

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. A000169, A000272, A000312, A007778, A007830, A008785, this sequence, A008787, A008788, A008789, A008790, A008791.

List([0..20], n-> (n+5)^n); # G. C. Greubel, Sep 11 2019

[(n+5)^n: n in [0..20]]; // Vincenzo Librandi, Jun 11 2013

Table[(n+5)^n,{n,0,20}] (* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

vector(20, n, (n+4)^(n-1)) \\ G. C. Greubel, Sep 11 2019

[(n+5)^n for n in (0..20)] # G. C. Greubel, Sep 11 2019

E.g.f.(x) for b(n) = n^(n-5) = a(n-5): T - (15/16)*T^2 + (85/216)T^3 - (25/288)*T^4 + (1/120)*T^5, where T=T(x) is Euler's tree function. - Len Smiley, Nov 17 2001
E.g.f.: LambertW(-x)^5/((-x)^5*(1+LambertW(-x))). - Vladeta Jovovic, Nov 07 2003
E.g.f.: (1/4)*d/dx((LambertW(-x)/(-x))^4). - Wolfdieter Lang, Oct 25 2022

A008787 a(n) = (n + 6)^n.

Original entry on oeis.org

1, 7, 64, 729, 10000, 161051, 2985984, 62748517, 1475789056, 38443359375, 1099511627776, 34271896307633, 1156831381426176, 42052983462257059, 1638400000000000000, 68122318582951682301, 3011361496339065143296

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. A000169, A000272, A000312, A007778, A007830, A008785, A008786, this sequence, A008788, A008789, A008790, A008791.

List([0..20], n-> (n+6)^n); # G. C. Greubel, Sep 11 2019

[(n+6)^n: n in [0..20]]; // Vincenzo Librandi, Jun 11 2013

Maple
```
a:= n-> (n+6)^n: seq(a(n), n=0..20);
```

Table[(n+6)^n,{n,0,20}] (* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

vector(20, n, (n+5)^(n-1)) \\ G. C. Greubel, Sep 11 2019

[(n+6)^n for n in (0..20)] # G. C. Greubel, Sep 11 2019

E.g.f.(x) for b(n) = n^(n-6) = a(n-6): T - (31/32)*T^2 + (575/1296)*T^3 - (415/3456)*T^4 + (137/7200)*T^5 - (1/720)*T^6; where T=T(x) is Euler's tree function (see A000169). - Len Smiley, Nov 17 2001
E.g.f.: LambertW(-x)^6/(x^6*(1+LambertW(-x))). - Vladeta Jovovic, Nov 07 2003
E.g.f.: (1/5)*d/dx(LambertW(-x)/(-x))^5. - Wolfdieter Lang, Oct 25 2022

A008790 a(n) = n^(n+4).

Original entry on oeis.org

0, 1, 64, 2187, 65536, 1953125, 60466176, 1977326743, 68719476736, 2541865828329, 100000000000000, 4177248169415651, 184884258895036416, 8650415919381337933, 426878854210636742656, 22168378200531005859375

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Cf. A000169, A000272, A000312, A007778, A007830, A008785, A008786, A008787, A008788, A008789, A008791.

List([0..20], n-> n^(n+4)); # G. C. Greubel, Sep 11 2019

[n^(n+4): n in [0..20]]; // Vincenzo Librandi, Jun 11 2013

a:=n->mul(n,k=-3..n):seq(a(n),n=0..20); # Zerinvary Lajos, Jan 26 2008

Table[n^(n+4),{n,0,20}](* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

vector(20, n, (n-1)^(n+3)) \\ G. C. Greubel, Sep 11 2019

[n^(n+4) for n in (0..20)] # G. C. Greubel, Sep 11 2019

E.g.f.: T*(1 +22*T +58*T^2 +24*T^3)*(1-T)^(-9); where T is Euler's tree function (see A000169). - Len Smiley, Nov 17 2001
See A008517 and A134991 for similar e.g.f.s and diagonals of A048993. - Tom Copeland, Oct 03 2011
E.g.f.: d^4/dx^4 {x^4/(T(x)^4*(1-T(x)))}, where T(x) = Sum_{n>=1} n^(n-1)*x^n/n! is the tree function of A000169. - Peter Bala, Aug 05 2012

cp's OEIS Frontend

A007778 a(n) = n^(n+1).

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A003992 Square array read by upwards antidiagonals: T(n,k) = n^k for n >= 0, k >= 0.

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A089072 Triangle read by rows: T(n,k) = k^n, n >= 1, 1 <= k <= n.

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A007830 a(n) = (n+3)^n.

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A008785 a(n) = (n+4)^n.

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A008791 a(n) = n^(n+5).

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